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G = C4×F11order 440 = 23·5·11

Direct product of C4 and F11

direct product, metacyclic, supersoluble, monomial, A-group

Aliases: C4×F11, D11⋊C20, C442C10, D22.C10, Dic112C10, (C4×D11)⋊C5, C11⋊C202C2, C111(C2×C20), (C2×F11).C2, C2.1(C2×F11), C22.2(C2×C10), C11⋊C51(C2×C4), (C4×C11⋊C5)⋊2C2, (C2×C11⋊C5).2C22, SmallGroup(440,8)

Series: Derived Chief Lower central Upper central

C1C11 — C4×F11
C1C11C22C2×C11⋊C5C2×F11 — C4×F11
C11 — C4×F11
C1C4

Generators and relations for C4×F11
 G = < a,b,c | a4=b11=c10=1, ab=ba, ac=ca, cbc-1=b6 >

11C2
11C2
11C5
11C4
11C22
11C10
11C10
11C10
11C2×C4
11C20
11C2×C10
11C20
11C2×C20

Smallest permutation representation of C4×F11
On 44 points
Generators in S44
(1 34 12 23)(2 35 13 24)(3 36 14 25)(4 37 15 26)(5 38 16 27)(6 39 17 28)(7 40 18 29)(8 41 19 30)(9 42 20 31)(10 43 21 32)(11 44 22 33)
(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 41 42 43 44)
(2 3 5 9 6 11 10 8 4 7)(13 14 16 20 17 22 21 19 15 18)(24 25 27 31 28 33 32 30 26 29)(35 36 38 42 39 44 43 41 37 40)

G:=sub<Sym(44)| (1,34,12,23)(2,35,13,24)(3,36,14,25)(4,37,15,26)(5,38,16,27)(6,39,17,28)(7,40,18,29)(8,41,19,30)(9,42,20,31)(10,43,21,32)(11,44,22,33), (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)(34,35,36,37,38,39,40,41,42,43,44), (2,3,5,9,6,11,10,8,4,7)(13,14,16,20,17,22,21,19,15,18)(24,25,27,31,28,33,32,30,26,29)(35,36,38,42,39,44,43,41,37,40)>;

G:=Group( (1,34,12,23)(2,35,13,24)(3,36,14,25)(4,37,15,26)(5,38,16,27)(6,39,17,28)(7,40,18,29)(8,41,19,30)(9,42,20,31)(10,43,21,32)(11,44,22,33), (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)(34,35,36,37,38,39,40,41,42,43,44), (2,3,5,9,6,11,10,8,4,7)(13,14,16,20,17,22,21,19,15,18)(24,25,27,31,28,33,32,30,26,29)(35,36,38,42,39,44,43,41,37,40) );

G=PermutationGroup([[(1,34,12,23),(2,35,13,24),(3,36,14,25),(4,37,15,26),(5,38,16,27),(6,39,17,28),(7,40,18,29),(8,41,19,30),(9,42,20,31),(10,43,21,32),(11,44,22,33)], [(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),(34,35,36,37,38,39,40,41,42,43,44)], [(2,3,5,9,6,11,10,8,4,7),(13,14,16,20,17,22,21,19,15,18),(24,25,27,31,28,33,32,30,26,29),(35,36,38,42,39,44,43,41,37,40)]])

44 conjugacy classes

class 1 2A2B2C4A4B4C4D5A5B5C5D10A···10L 11 20A···20P 22 44A44B
order12224444555510···101120···20224444
size1111111111111111111111···111011···11101010

44 irreducible representations

dim1111111111101010
type++++++
imageC1C2C2C2C4C5C10C10C10C20F11C2×F11C4×F11
kernelC4×F11C11⋊C20C4×C11⋊C5C2×F11F11C4×D11Dic11C44D22D11C4C2C1
# reps11114444416112

Matrix representation of C4×F11 in GL10(𝔽661)

555000000000
055500000000
005550000000
000555000000
000055500000
000005550000
000000555000
000000055500
000000005550
000000000555
,
000000000660
100000000660
010000000660
001000000660
000100000660
000010000660
000001000660
000000100660
000000010660
000000001660
,
100006600000
000006601000
010006600000
000006600100
001006600000
000006600010
000106600000
000006600001
000016600000
000006600000

G:=sub<GL(10,GF(661))| [555,0,0,0,0,0,0,0,0,0,0,555,0,0,0,0,0,0,0,0,0,0,555,0,0,0,0,0,0,0,0,0,0,555,0,0,0,0,0,0,0,0,0,0,555,0,0,0,0,0,0,0,0,0,0,555,0,0,0,0,0,0,0,0,0,0,555,0,0,0,0,0,0,0,0,0,0,555,0,0,0,0,0,0,0,0,0,0,555,0,0,0,0,0,0,0,0,0,0,555],[0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,660,660,660,660,660,660,660,660,660,660],[1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,660,660,660,660,660,660,660,660,660,660,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0] >;

C4×F11 in GAP, Magma, Sage, TeX

C_4\times F_{11}
% in TeX

G:=Group("C4xF11");
// GroupNames label

G:=SmallGroup(440,8);
// by ID

G=gap.SmallGroup(440,8);
# by ID

G:=PCGroup([5,-2,-2,-5,-2,-11,106,10004,2264]);
// Polycyclic

G:=Group<a,b,c|a^4=b^11=c^10=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^6>;
// generators/relations

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Subgroup lattice of C4×F11 in TeX

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