#27079753

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

Aliases

No aliases for this group.

Splittings

Fitting	C₄₇×#2883 ⋊ C₂
Sylow	C₄₇ ⋊ #60070

Subgroups

	subgroup	G/H
center	C₂	C₂²×C₂²⋊C₄×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₄₇
Fitting	C₄₇×#2883	C₂
socle	C₂×C₄₇	C₂³×C₂²⋊C₄
prime radical	C₂×#15689958	C₂
cosocle	C₂³×C₄₇	C₂⁵
hypercenter	#2883	D₄₇
hypocenter	C₄₇	#60070
LCS	G ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂²×D₄ ◁ #2883

4892 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:

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

Polycyclic presentation:

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

Conjugacy classes & character table

1025 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1033043);