#27080213

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

No aliases for this group.

Splittings

Fitting	C₄₇×#2933 ⋊ C₂
Sylow	C₄₇ ⋊ #60142

Subgroups

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁴×C₄
Fitting	C₄₇×#2933	C₂
prime radical	#20256718	C₂
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	#2933	D₄₇
hypocenter	C₄₇	#60142
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #2933

2714 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 83
transitive degree	μ_t(G) = 3008

A minimal faithful permutation representation — 5 generators on 83 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)(53,60)(58,69)(59,71)(61,73)(68,78)(70,80)(72,81)(79,83);(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)(54,63)(55,65)(58,69)(59,71)(64,76)(66,77)(70,80)(72,81);(52,55,56,66,57,65,67,77)(53,59,61,72,60,71,73,81)(54,62,64,74,63,75,76,82)(58,68,70,79,69,78,80,83);(49,51)(52,54)(53,58)(55,62)(56,64)(57,63)(59,68)(60,69)(61,70)(65,75)(66,74)(67,76)(71,78)(72,79)(73,80)(77,82)(81,83);(48,49)(50,51)(52,53,56,61,57,60,67,73)(54,58,64,70,63,69,76,80)(55,59,66,72,65,71,77,81)(62,68,74,79,75,78,82,83)

Polycyclic presentation:

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

Conjugacy classes & character table

1238 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1033503);