C₂⁶×#64408 #34032724

order	18688
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₄ · Schur multiplier (H₂) = C₂²¹

Aliases

direct product	C₂⁶×#64408
unambiguous semidirect product	D₇₃⋊(C₂⁵×C₄)

Splittings

Fitting, socle	C₂⁶×C₇₃ ⋊ C₄
derived, Sylow	C₇₃ ⋊ C₂⁶×C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂⁶	#64408
commutator, hypocenter	C₇₃	C₂⁶×C₄
Frattini	C₁	G
Fitting, socle	C₂⁶×C₇₃	C₄
prime radical	C₂⁶×D₇₃	C₂
cosocle	D₇₃	C₂⁷
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₂⁶

111198 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 85
transitive degree	μ_t(G) = 4672

A minimal faithful permutation representation — 7 generators on 85 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)(31,42,43,57)(35,46,47,53)(39,50,51,49)(41,54,55,45)(44,59,60,72)(48,63,64,73)(52,61,67,69)(56,70,71,66)(58,74,75,62)(65,76,77,81)(68,78,79,82)(80,83,84,85);(11,12)(13,14,17,22,31,44,61,46,29,41,56,72,81,85,84,79,67,51,38,27,36,49,66,74,54,37,24,15,19,26,35,48,65,78,63,42,58,75,57,73,82,77,64,47,34,25,18,23,32,45,62,70,50,33,20,28,39,52,68,80,83,76,59,71,55,40,53,69,60,43,30,21,16);(9,10);(7,8);(5,6);(3,4);(1,2)

Conjugacy classes & character table

1408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1116308);

C26×#64408 #34032724