#27081284

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁸

Aliases

No aliases for this group.

Splittings

Sylow

C₄₇ ⋊ #60252

Subgroups

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁴×C₄
Fitting	C₄₇×#2924	C₂
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	#2924	D₄₇
hypocenter	C₄₇	#60252
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #2924

1626 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 95
transitive degree	μ_t(G) = 3008

A minimal faithful permutation representation — 5 generators on 95 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)(66,75)(70,81)(74,86)(76,88)(80,90)(82,92)(87,94)(91,95);(49,55)(53,56)(54,63)(61,62)(67,77)(71,83)(74,86)(78,89)(80,90)(84,93)(87,94)(91,95);(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)(48,51,52,60)(49,54,55,63)(50,57,58,59)(53,61,56,62)(64,67)(65,71)(66,74)(68,78)(69,77)(70,80)(72,84)(73,83)(75,86)(76,87)(79,89)(81,90)(82,91)(85,93)(88,94)(92,95);(48,50,52,58)(49,53,55,56)(51,59,60,57)(54,62,63,61)(64,66)(65,70)(67,74)(68,76)(69,75)(71,80)(72,82)(73,81)(77,86)(78,87)(79,88)(83,90)(84,91)(85,92)(89,94)(93,95);(48,49)(50,56)(51,54)(52,55)(53,58)(57,62)(59,61)(60,63)(64,65,68,72,69,73,79,85)(66,70,76,82,75,81,88,92)(67,71,78,84,77,83,89,93)(74,80,87,91,86,90,94,95)

Polycyclic presentation:

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

Conjugacy classes & character table

1226 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1034574);