#27083646

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

Aliases

No aliases for this group.

Splittings

Fitting	C₄₇×#2912 ⋊ C₂
Sylow	C₄₇ ⋊ #60462

Subgroups

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#2912	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#2912	D₄₇
hypocenter	C₄₇	#60462
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×#41 ◁ #2912

2666 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:

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

Polycyclic presentation:

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

Conjugacy classes & character table

1070 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1036936);