direct product, abelian, monomial, 2-elementary
Aliases: C22xC10, SmallGroup(40,14)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C22xC10 |
| C1 — C22xC10 |
| C1 — C22xC10 |
Generators and relations for C22xC10
G = < a,b,c | a2=b2=c10=1, ab=ba, ac=ca, bc=cb >
Quotients: C1, C2, C22, C5, C23, C10, C2xC10, C22xC10
Smallest permutation representation of C22xC10
►Regular action on 40 points
Generators in S40
(1 27)(2 28)(3 29)(4 30)(5 21)(6 22)(7 23)(8 24)(9 25)(10 26)(11 31)(12 32)(13 33)(14 34)(15 35)(16 36)(17 37)(18 38)(19 39)(20 40)
(1 17)(2 18)(3 19)(4 20)(5 11)(6 12)(7 13)(8 14)(9 15)(10 16)(21 31)(22 32)(23 33)(24 34)(25 35)(26 36)(27 37)(28 38)(29 39)(30 40)
(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 29 30)(31 32 33 34 35 36 37 38 39 40)
G:=sub<Sym(40)| (1,27)(2,28)(3,29)(4,30)(5,21)(6,22)(7,23)(8,24)(9,25)(10,26)(11,31)(12,32)(13,33)(14,34)(15,35)(16,36)(17,37)(18,38)(19,39)(20,40), (1,17)(2,18)(3,19)(4,20)(5,11)(6,12)(7,13)(8,14)(9,15)(10,16)(21,31)(22,32)(23,33)(24,34)(25,35)(26,36)(27,37)(28,38)(29,39)(30,40), (1,2,3,4,5,6,7,8,9,10)(11,12,13,14,15,16,17,18,19,20)(21,22,23,24,25,26,27,28,29,30)(31,32,33,34,35,36,37,38,39,40)>;
G:=Group( (1,27)(2,28)(3,29)(4,30)(5,21)(6,22)(7,23)(8,24)(9,25)(10,26)(11,31)(12,32)(13,33)(14,34)(15,35)(16,36)(17,37)(18,38)(19,39)(20,40), (1,17)(2,18)(3,19)(4,20)(5,11)(6,12)(7,13)(8,14)(9,15)(10,16)(21,31)(22,32)(23,33)(24,34)(25,35)(26,36)(27,37)(28,38)(29,39)(30,40), (1,2,3,4,5,6,7,8,9,10)(11,12,13,14,15,16,17,18,19,20)(21,22,23,24,25,26,27,28,29,30)(31,32,33,34,35,36,37,38,39,40) );
G=PermutationGroup([[(1,27),(2,28),(3,29),(4,30),(5,21),(6,22),(7,23),(8,24),(9,25),(10,26),(11,31),(12,32),(13,33),(14,34),(15,35),(16,36),(17,37),(18,38),(19,39),(20,40)], [(1,17),(2,18),(3,19),(4,20),(5,11),(6,12),(7,13),(8,14),(9,15),(10,16),(21,31),(22,32),(23,33),(24,34),(25,35),(26,36),(27,37),(28,38),(29,39),(30,40)], [(1,2,3,4,5,6,7,8,9,10),(11,12,13,14,15,16,17,18,19,20),(21,22,23,24,25,26,27,28,29,30),(31,32,33,34,35,36,37,38,39,40)]])
C22xC10 is a maximal subgroup of
C23.D5
40 conjugacy classes
| class | 1 | 2A | ··· | 2G | 5A | 5B | 5C | 5D | 10A | ··· | 10AB |
| order | 1 | 2 | ··· | 2 | 5 | 5 | 5 | 5 | 10 | ··· | 10 |
| size | 1 | 1 | ··· | 1 | 1 | 1 | 1 | 1 | 1 | ··· | 1 |
40 irreducible representations
| dim | 1 | 1 | 1 | 1 |
| type | + | + | ||
| image | C1 | C2 | C5 | C10 |
| kernel | C22xC10 | C2xC10 | C23 | C22 |
| # reps | 1 | 7 | 4 | 28 |
Matrix representation of C22xC10 ►in GL3(F11) generated by
| 10 | 0 | 0 |
| 0 | 1 | 0 |
| 0 | 0 | 1 |
| 10 | 0 | 0 |
| 0 | 10 | 0 |
| 0 | 0 | 1 |
| 1 | 0 | 0 |
| 0 | 1 | 0 |
| 0 | 0 | 2 |
G:=sub<GL(3,GF(11))| [10,0,0,0,1,0,0,0,1],[10,0,0,0,10,0,0,0,1],[1,0,0,0,1,0,0,0,2] >;
C22xC10 in GAP, Magma, Sage, TeX
C_2^2\times C_{10} % in TeX
G:=Group("C2^2xC10"); // GroupNames label
G:=SmallGroup(40,14);
// by ID
G=gap.SmallGroup(40,14);
# by ID
G:=PCGroup([4,-2,-2,-2,-5]);
// Polycyclic
G:=Group<a,b,c|a^2=b^2=c^10=1,a*b=b*a,a*c=c*a,b*c=c*b>;
// generators/relations
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