#27113388

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁸

Aliases

No aliases for this group.

Splittings

Fitting	C₄₇×#3555 ⋊ C₂
Sylow	C₄₇ ⋊ #62172

Subgroups

	subgroup	G/H
center	C₂²	C₂³×C₂²⋊D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3555	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	#20257460	C₂
hypercenter	#3555	D₄₇
hypocenter	C₄₇	#62172
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #529 ◁ #3555

1652 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 95
transitive degree	μ_t(G) = 3008

A minimal faithful permutation representation — 5 generators on 95 points:

(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(48,51,52,60)(49,54,55,59)(50,58,57,63)(53,61,56,62)(65,74)(66,78)(72,89)(73,83)(76,93)(77,82)(79,88)(92,94);(50,57)(53,56)(58,63)(61,62)(64,68,69,70)(65,73,74,83)(66,77,78,82)(67,80,81,84)(71,86,75,87)(72,88,89,79)(76,92,93,94)(85,95,90,91);(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)(64,67)(65,72)(66,76)(68,80)(69,81)(70,84)(71,85)(73,88)(74,89)(75,90)(77,92)(78,93)(79,83)(82,94)(86,95)(87,91);(48,50)(49,53)(51,58)(52,57)(54,61)(55,56)(59,62)(60,63)(64,66)(65,71)(67,76)(68,82)(69,78)(70,77)(72,85)(73,87)(74,75)(79,95)(80,94)(81,93)(83,86)(84,92)(88,91)(89,90);(48,49,52,55)(50,56,57,53)(51,59,60,54)(58,61,63,62)(64,65)(66,75)(67,79)(68,73)(69,74)(70,83)(71,78)(72,80)(76,91)(77,87)(81,88)(82,86)(84,89)(85,92)(90,94)(93,95)

Polycyclic presentation:

2^8,47|a^2=fh,d^2=h,e^2=fh,g^2=h,b^a=bf,c^a=cg,e^a=ef,g^a=gh,d^b=df,e^b=eh,g^c=gh,i^c=i^46

Conjugacy classes & character table

923 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1066678);