#27092595

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

Aliases

No aliases for this group.

Splittings

Fitting	C₄₇×#2956 ⋊ C₂
Sylow	C₄₇ ⋊ #61111

Subgroups

	subgroup	G/H
center	C₂	C₂×D₄×D₁₈₈
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#2956	C₂
socle	C₂×C₄₇	C₂×D₄²
hypercenter	#2956	D₄₇
hypocenter	C₄₇	#61111
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #2956

2600 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 79
transitive degree	μ_t(G) = 1504

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

Polycyclic presentation:

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

Conjugacy classes & character table

1064 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1045885);