#27079882

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹⁰

Aliases

No aliases for this group.

Splittings

Sylow

C₄₇ ⋊ #60093

Subgroups

	subgroup	G/H
center	C₄	C₂³×C₂²⋊D₄₇
commutator	C₄×C₄₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting, prime radical	C₂×C₄₇×#585	C₂
socle	C₂×C₄₇	C₂³×C₂²⋊C₄
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	C₂×#585	D₄₇
hypocenter	C₄₇	#60093
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂²×#41 ◁ C₂×#585

4852 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)(49,57)(55,69)(56,71)(58,66)(59,70)(68,78)(72,76)(73,79);(51,63)(56,71)(60,74)(64,65)(68,78)(72,76)(73,79)(75,77);(48,51)(49,56)(50,60)(52,64)(53,65)(54,63)(55,68)(57,71)(58,72)(59,73)(61,75)(62,74)(66,76)(67,77)(69,78)(70,79);(48,50)(49,55)(51,60)(52,67)(53,61)(54,62)(56,68)(57,69)(58,70)(59,66)(63,74)(64,77)(65,75)(71,78)(72,79)(73,76);(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)(48,49,53,58,54,57,52,66)(50,59,61,55,62,70,67,69)(51,56,65,72,63,71,64,76)(60,73,75,68,74,79,77,78)

Polycyclic presentation:

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

Conjugacy classes & character table

1646 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1033172);