#27080067

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁷×C₄

Aliases

No aliases for this group.

Splittings

Fitting	C₄₇×#2922 ⋊ C₂
Sylow	C₄₇ ⋊ #60126

Subgroups

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁴×C₄
Fitting	C₄₇×#2922	C₂
prime radical	C₂×#41×D₄₇	C₂²
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	#2922	D₄₇
hypocenter	C₄₇	#60126
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #2922

2042 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 87
transitive degree	μ_t(G) = 3008

A minimal faithful permutation representation — 5 generators on 87 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)(58,67)(62,73)(66,78)(68,80)(72,82)(74,84)(79,86)(83,87);(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)(59,69)(63,75)(66,78)(70,81)(72,82)(76,85)(79,86)(83,87);(48,50,51,54)(49,53,52,55)(56,59)(57,63)(58,66)(60,70)(61,69)(62,72)(64,76)(65,75)(67,78)(68,79)(71,81)(73,82)(74,83)(77,85)(80,86)(84,87);(49,52)(53,55)(56,58)(57,62)(59,66)(60,68)(61,67)(63,72)(64,74)(65,73)(69,78)(70,79)(71,80)(75,82)(76,83)(77,84)(81,86)(85,87);(48,49)(50,53)(51,52)(54,55)(56,57,60,64,61,65,71,77)(58,62,68,74,67,73,80,84)(59,63,70,76,69,75,81,85)(66,72,79,83,78,82,86,87)

Polycyclic presentation:

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

Conjugacy classes & character table

1376 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1033357);