#27124789

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂⁶ · Schur multiplier (H₂) = C₂¹³

Aliases

No aliases for this group.

Splittings

Fitting	C₄₇×#3495 ⋊ C₂
Sylow	C₄₇ ⋊ #62810

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₄₇
commutator, socle, cosocle	C₂²×C₄₇	C₂⁶
Fitting	C₄₇×#3495	C₂
hypercenter	#3495	D₄₇
hypocenter	C₄₇	#62810
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #3495

7220 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 71
transitive degree	μ_t(G) = 3008

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

(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)(45,46)(48,50,51,54)(49,53,52,55)(56,60,61,58)(57,62,64,65)(59,69,68,66)(63,70,67,71);(56,58,61,60)(57,62,64,65)(59,66,68,69)(63,70,67,71);(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)(44,45)(46,47)(59,68)(63,67)(66,69)(70,71);(56,59)(57,63)(58,66)(60,69)(61,68)(62,70)(64,67)(65,71);(49,52)(53,55)(56,58,61,60)(57,62,64,65)(59,66,68,69)(63,70,67,71);(48,49)(50,53)(51,52)(54,55)(56,57)(58,65)(59,67)(60,62)(61,64)(63,68)(66,70)(69,71)

Polycyclic presentation:

2^8,47|b^2=h,e^2=h,f^2=g,b^a=bg,c^a=ch,e^a=eh,d^c=dh,i^d=i^46,i^f=i^46

Conjugacy classes & character table

1100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1078079);