#27083243

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁹

Aliases

No aliases for this group.

Splittings

Fitting	C₄₇×#3043 ⋊ C₂
Sylow	C₄₇ ⋊ #60424

Subgroups

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3043	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	#20256719	C₂
hypercenter	#3043	D₄₇
hypocenter	C₄₇	#60424
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3043

2674 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:

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

Polycyclic presentation:

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

Conjugacy classes & character table

794 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1036533);