#27088528

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

Aliases

No aliases for this group.

Splittings

Fitting	C₄₇×#3243 ⋊ C₂
Sylow	C₄₇ ⋊ #60859

Subgroups

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3243	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	#20256775	C₂
hypercenter	#3243	D₄₇
hypocenter	C₄₇	#60859
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3243

1654 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)(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)(64,68,70,69)(65,73,74,82)(66,77,76,78)(67,80,81,83)(71,86,85,92)(72,87,88,79)(75,91,90,93)(84,95,94,89);(49,55)(53,56)(54,63)(61,62)(66,76)(71,85)(75,90)(77,78)(84,94)(86,92)(89,95)(91,93);(48,51,52,60)(49,54,55,63)(50,57,58,59)(53,61,56,62)(64,67)(65,72)(66,75)(68,80)(69,83)(70,81)(71,84)(73,87)(74,88)(76,90)(77,91)(78,93)(79,82)(85,94)(86,95)(89,92);(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)(48,50,52,58)(49,53,55,56)(51,59,60,57)(54,62,63,61)(64,66)(65,71)(67,75)(68,77)(69,78)(70,76)(72,84)(73,86)(74,85)(79,89)(80,91)(81,90)(82,92)(83,93)(87,95)(88,94);(48,49)(50,56)(51,54)(52,55)(53,58)(57,62)(59,61)(60,63)(64,65)(66,71)(67,79)(68,73)(69,82)(70,74)(72,80)(75,89)(76,85)(77,86)(78,92)(81,87)(83,88)(84,91)(90,95)(93,94)

Polycyclic presentation:

2^8,47|b^2=f,c^2=f,e^2=h,g^2=h,b^a=bf,c^a=cg,d^a=df,g^a=gh,c^b=cf,d^b=dh,i^b=i^46,g^c=gh,i^e=i^46

Conjugacy classes & character table

650 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1041818);