metabelian, soluble, monomial, A-group
Aliases: C26⋊2C7, C23⋊1F8, SmallGroup(448,1393)
Series: Derived ►Chief ►Lower central ►Upper central
C26 — C26⋊C7 |
Subgroups: 2962 in 424 conjugacy classes, 12 normal (3 characteristic)
C1, C2 [×9], C22 [×93], C7, C23 [×9], C23 [×198], C24 [×93], C25 [×9], F8 [×9], C26, C26⋊C7
Quotients:
C1, C7, F8 [×9], C26⋊C7
Generators and relations
G = < a,b,c,d,e,f,g | a2=b2=c2=d2=e2=f2=g7=1, ab=ba, ac=ca, ad=da, ae=ea, af=fa, gag-1=cb=bc, bd=db, be=eb, bf=fb, gbg-1=a, cd=dc, ce=ec, cf=fc, gcg-1=b, de=ed, df=fd, gdg-1=fe=ef, geg-1=d, gfg-1=e >
(1 12)(2 25)(4 16)(5 28)(6 18)(7 11)(8 27)(9 17)(10 22)(13 21)(19 23)(20 24)
(1 12)(2 13)(3 26)(5 17)(6 22)(7 19)(9 28)(10 18)(11 23)(14 15)(20 24)(21 25)
(1 20)(2 13)(3 14)(4 27)(6 18)(7 23)(8 16)(10 22)(11 19)(12 24)(15 26)(21 25)
(1 12)(4 8)(6 10)(7 11)(16 27)(18 22)(19 23)(20 24)
(1 12)(2 13)(5 9)(7 11)(17 28)(19 23)(20 24)(21 25)
(1 12)(2 13)(3 14)(6 10)(15 26)(18 22)(20 24)(21 25)
(1 2 3 4 5 6 7)(8 9 10 11 12 13 14)(15 16 17 18 19 20 21)(22 23 24 25 26 27 28)
G:=sub<Sym(28)| (1,12)(2,25)(4,16)(5,28)(6,18)(7,11)(8,27)(9,17)(10,22)(13,21)(19,23)(20,24), (1,12)(2,13)(3,26)(5,17)(6,22)(7,19)(9,28)(10,18)(11,23)(14,15)(20,24)(21,25), (1,20)(2,13)(3,14)(4,27)(6,18)(7,23)(8,16)(10,22)(11,19)(12,24)(15,26)(21,25), (1,12)(4,8)(6,10)(7,11)(16,27)(18,22)(19,23)(20,24), (1,12)(2,13)(5,9)(7,11)(17,28)(19,23)(20,24)(21,25), (1,12)(2,13)(3,14)(6,10)(15,26)(18,22)(20,24)(21,25), (1,2,3,4,5,6,7)(8,9,10,11,12,13,14)(15,16,17,18,19,20,21)(22,23,24,25,26,27,28)>;
G:=Group( (1,12)(2,25)(4,16)(5,28)(6,18)(7,11)(8,27)(9,17)(10,22)(13,21)(19,23)(20,24), (1,12)(2,13)(3,26)(5,17)(6,22)(7,19)(9,28)(10,18)(11,23)(14,15)(20,24)(21,25), (1,20)(2,13)(3,14)(4,27)(6,18)(7,23)(8,16)(10,22)(11,19)(12,24)(15,26)(21,25), (1,12)(4,8)(6,10)(7,11)(16,27)(18,22)(19,23)(20,24), (1,12)(2,13)(5,9)(7,11)(17,28)(19,23)(20,24)(21,25), (1,12)(2,13)(3,14)(6,10)(15,26)(18,22)(20,24)(21,25), (1,2,3,4,5,6,7)(8,9,10,11,12,13,14)(15,16,17,18,19,20,21)(22,23,24,25,26,27,28) );
G=PermutationGroup([(1,12),(2,25),(4,16),(5,28),(6,18),(7,11),(8,27),(9,17),(10,22),(13,21),(19,23),(20,24)], [(1,12),(2,13),(3,26),(5,17),(6,22),(7,19),(9,28),(10,18),(11,23),(14,15),(20,24),(21,25)], [(1,20),(2,13),(3,14),(4,27),(6,18),(7,23),(8,16),(10,22),(11,19),(12,24),(15,26),(21,25)], [(1,12),(4,8),(6,10),(7,11),(16,27),(18,22),(19,23),(20,24)], [(1,12),(2,13),(5,9),(7,11),(17,28),(19,23),(20,24),(21,25)], [(1,12),(2,13),(3,14),(6,10),(15,26),(18,22),(20,24),(21,25)], [(1,2,3,4,5,6,7),(8,9,10,11,12,13,14),(15,16,17,18,19,20,21),(22,23,24,25,26,27,28)])
G:=TransitiveGroup(28,60);
Matrix representation ►G ⊆ GL14(𝔽29)
28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 8 | 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
8 | 28 | 28 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
7 | 28 | 21 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 28 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 28 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 27 | 15 | 0 | 0 | 28 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 27 | 15 | 0 | 1 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 15 | 2 | 0 | 0 | 0 | 0 | 28 |
28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 7 | 0 | 21 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
8 | 28 | 0 | 22 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 8 | 0 | 0 | 0 | 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 28 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 28 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 28 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 14 | 27 | 13 | 1 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 13 | 0 | 0 | 0 | 0 | 28 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 27 | 13 | 2 | 0 | 0 | 1 |
28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 28 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 1 | 0 | 7 | 0 | 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 1 | 0 | 28 | 0 | 0 | 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 28 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 28 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 28 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 16 | 28 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 16 | 27 | 27 | 0 | 0 | 1 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 14 | 27 | 13 | 0 | 0 | 0 | 1 |
28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 8 | 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
8 | 28 | 28 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
7 | 28 | 21 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 7 | 0 | 21 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
8 | 28 | 0 | 22 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 8 | 0 | 0 | 0 | 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 28 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 1 | 0 | 7 | 0 | 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 1 | 0 | 28 | 0 | 0 | 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
28 | 22 | 1 | 8 | 27 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 21 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 22 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 28 | 22 | 1 | 8 | 28 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 21 | 1 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 22 | 0 | 1 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
G:=sub<GL(14,GF(29))| [28,0,0,0,0,8,7,0,0,0,0,0,0,0,0,28,0,0,0,28,28,0,0,0,0,0,0,0,0,0,28,0,0,28,21,0,0,0,0,0,0,0,0,0,0,1,8,0,0,0,0,0,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,27,0,15,0,0,0,0,0,0,0,0,1,0,0,15,0,2,0,0,0,0,0,0,0,0,0,28,0,0,27,0,0,0,0,0,0,0,0,0,0,0,28,0,15,0,0,0,0,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,28],[28,0,0,0,1,8,0,0,0,0,0,0,0,0,0,28,0,0,7,28,0,0,0,0,0,0,0,0,0,0,1,0,0,0,8,0,0,0,0,0,0,0,0,0,0,28,21,22,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,13,0,0,0,0,0,0,0,0,0,28,0,0,14,0,27,0,0,0,0,0,0,0,0,0,28,0,27,0,13,0,0,0,0,0,0,0,0,0,0,28,13,0,2,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1],[28,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,28,0,28,0,0,0,0,0,0,0,0,0,0,0,0,1,0,7,28,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,0,0,0,0,0,0,28,0,0,0,0,16,14,0,0,0,0,0,0,0,0,28,0,0,0,27,27,0,0,0,0,0,0,0,0,0,28,0,0,27,13,0,0,0,0,0,0,0,0,0,0,1,16,0,0,0,0,0,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1],[28,0,0,0,0,8,7,0,0,0,0,0,0,0,0,28,0,0,0,28,28,0,0,0,0,0,0,0,0,0,28,0,0,28,21,0,0,0,0,0,0,0,0,0,0,1,8,0,0,0,0,0,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1],[28,0,0,0,1,8,0,0,0,0,0,0,0,0,0,28,0,0,7,28,0,0,0,0,0,0,0,0,0,0,1,0,0,0,8,0,0,0,0,0,0,0,0,0,0,28,21,22,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1],[28,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,28,0,28,0,0,0,0,0,0,0,0,0,0,0,0,1,0,7,28,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1],[0,0,0,28,0,0,0,0,0,0,0,0,0,0,1,0,0,22,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,8,0,0,0,0,0,0,0,0,0,0,0,0,0,27,21,22,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,0,0,1,0,0,22,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,8,0,0,0,0,0,0,0,0,0,0,0,0,0,28,21,22,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0] >;
Character table of C26⋊C7
class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 7A | 7B | 7C | 7D | 7E | 7F | |
size | 1 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 64 | 64 | 64 | 64 | 64 | 64 | |
ρ1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | trivial |
ρ2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ζ73 | ζ76 | ζ72 | ζ75 | ζ7 | ζ74 | linear of order 7 |
ρ3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ζ75 | ζ73 | ζ7 | ζ76 | ζ74 | ζ72 | linear of order 7 |
ρ4 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ζ72 | ζ74 | ζ76 | ζ7 | ζ73 | ζ75 | linear of order 7 |
ρ5 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ζ74 | ζ7 | ζ75 | ζ72 | ζ76 | ζ73 | linear of order 7 |
ρ6 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ζ7 | ζ72 | ζ73 | ζ74 | ζ75 | ζ76 | linear of order 7 |
ρ7 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ζ76 | ζ75 | ζ74 | ζ73 | ζ72 | ζ7 | linear of order 7 |
ρ8 | 7 | -1 | -1 | -1 | 7 | -1 | -1 | -1 | -1 | -1 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from F8 |
ρ9 | 7 | -1 | -1 | -1 | -1 | -1 | -1 | 7 | -1 | -1 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from F8 |
ρ10 | 7 | -1 | -1 | -1 | -1 | -1 | 7 | -1 | -1 | -1 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from F8 |
ρ11 | 7 | -1 | -1 | 7 | -1 | -1 | -1 | -1 | -1 | -1 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from F8 |
ρ12 | 7 | -1 | -1 | -1 | -1 | 7 | -1 | -1 | -1 | -1 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from F8 |
ρ13 | 7 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 7 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from F8 |
ρ14 | 7 | -1 | 7 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from F8 |
ρ15 | 7 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 7 | -1 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from F8 |
ρ16 | 7 | 7 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from F8 |
In GAP, Magma, Sage, TeX
C_2^6\rtimes C_7
% in TeX
G:=Group("C2^6:C7");
// GroupNames label
G:=SmallGroup(448,1393);
// by ID
G=gap.SmallGroup(448,1393);
# by ID
G:=PCGroup([7,-7,-2,2,2,-2,2,2,197,590,983,3924,9413,13726]);
// Polycyclic
G:=Group<a,b,c,d,e,f,g|a^2=b^2=c^2=d^2=e^2=f^2=g^7=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,a*f=f*a,g*a*g^-1=c*b=b*c,b*d=d*b,b*e=e*b,b*f=f*b,g*b*g^-1=a,c*d=d*c,c*e=e*c,c*f=f*c,g*c*g^-1=b,d*e=e*d,d*f=f*d,g*d*g^-1=f*e=e*f,g*e*g^-1=d,g*f*g^-1=e>;
// generators/relations