C₂⁶×#6157 #28330832

order	13568
isoclinism	isoclinic class of #6157
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₄ · Schur multiplier (H₂) = C₂²¹

Aliases

direct product	C₂⁶×#6157
unambiguous semidirect product	D₅₃⋊(C₂⁵×C₄)

Splittings

Fitting, socle	C₂⁶×C₅₃ ⋊ C₄
derived, Sylow	C₅₃ ⋊ C₂⁶×C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂⁶	#6157
commutator, hypocenter	C₅₃	C₂⁶×C₄
Frattini	C₁	G
Fitting, socle	C₂⁶×C₅₃	C₄
prime radical	C₂⁶×D₅₃	C₂
cosocle	D₅₃	C₂⁷
LCS	G ▷ C₅₃
UCS	C₁ ◁ C₂⁶

111198 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 65
transitive degree	μ_t(G) = 3392

A minimal faithful permutation representation — 7 generators on 65 points:

(14,15,16,18)(17,20,21,27)(19,24,25,23)(22,29,30,40)(26,33,34,36)(28,37,38,32)(31,42,43,55)(35,46,47,52)(39,44,50,49)(41,53,54,45)(48,56,57,62)(51,58,59,61)(60,63,64,65);(11,12)(13,14,17,22,31,44,33,20,28,39,51,60,63,56,42,54,40,52,61,57,47,34,25,18,23,32,45,53,37,24,15,19,26,35,48,58,46,29,41,55,62,65,64,59,50,38,27,36,49,43,30,21,16);(9,10);(7,8);(5,6);(3,4);(1,2)

Conjugacy classes & character table

1088 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1116308);

C26×#6157 #28330832