C₂⁵×#92420 #30626735

order	15616
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₈ · Schur multiplier (H₂) = C₂¹⁵

Aliases

direct product

C₂⁵×#92420

Splittings

derived, Sylow

C₆₁ ⋊ C₂⁵×C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₂⁶	#6923
commutator, hypocenter	C₆₁	C₂⁵×C₈
Frattini	C₂	C₂⁵×#6923
Fitting, socle, prime radical	C₂⁶×C₆₁	C₄
cosocle	Dic₆₁	C₂⁶
LCS	G ▷ C₆₁
UCS	C₁ ◁ C₂⁶

15454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 79
transitive degree	μ_t(G) = 15616

A minimal faithful permutation representation — 6 generators on 79 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)(37,48,49,63)(41,52,53,59)(45,56,57,55)(47,60,61,51)(50,65,66,67)(54,69,70,78)(58,73,74,76)(62,77,75,72)(64,79,71,68);(9,10)(19,20,23,28,37,50,67,79,60,43,30,21,25,32,41,54,71,63,78,77,56,39,26,34,45,58,75,61,46,59,76,73,52,35,47,62,74,57,44,33,42,55,72,69,48,64,70,53,40,31,24,29,38,51,68,65,66,49,36,27,22);(7,8);(5,6);(3,4);(1,2)

Conjugacy classes & character table

1216 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1116290);

C25×#92420 #30626735