C₂⁵×#88324 #28330814

order	13568
isoclinism	isoclinic class of #6157
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₈ · Schur multiplier (H₂) = C₂¹⁵

Aliases

direct product

C₂⁵×#88324

Splittings

derived, Sylow

C₅₃ ⋊ C₂⁵×C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₂⁶	#6157
commutator, hypocenter	C₅₃	C₂⁵×C₈
Frattini	C₂	C₂⁵×#6157
Fitting, socle, prime radical	C₂⁶×C₅₃	C₄
cosocle	Dic₅₃	C₂⁶
LCS	G ▷ C₅₃
UCS	C₁ ◁ C₂⁶

15454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 71
transitive degree	μ_t(G) = 13568

A minimal faithful permutation representation — 6 generators on 71 points:

(11,12,13,15,14,16,17,18)(20,21,22,24)(23,26,27,33)(25,30,31,29)(28,35,36,46)(32,39,40,42)(34,43,44,38)(37,48,49,61)(41,52,53,58)(45,50,56,55)(47,59,60,51)(54,62,63,68)(57,64,65,67)(66,69,70,71);(9,10)(19,20,23,28,37,50,39,26,34,45,57,66,69,62,48,60,46,58,67,63,53,40,31,24,29,38,51,59,43,30,21,25,32,41,54,64,52,35,47,61,68,71,70,65,56,44,33,42,55,49,36,27,22);(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, 1116290);

C25×#88324 #28330814