D₄₇×#3028 #27083014

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹⁰

Aliases

direct product

D₄₇×#3028

Splittings

Fitting	C₄₇×#3028 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#3028

Subgroups

	subgroup	G/H
center	C₂	C₂×#120×D₄₇
commutator, cosocle	C₂³×C₄₇	C₂⁵
Frattini	C₂³	C₂⁴×D₄₇
Fitting	C₄₇×#3028	C₂
socle	C₂×C₄₇	C₂²×#120
prime radical	#585×D₄₇	C₂
hypercenter	#3028	D₄₇
hypocenter	C₄₇	C₂×#3028
LCS	G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #3028

4790 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)(48,52,53,64)(49,56,57,63)(50,59,60,74)(51,61,62,76)(54,66,67,73)(55,68,69,75)(58,71,72,79)(65,77,70,78);(48,51)(49,55)(50,58)(52,61)(53,62)(54,65)(56,68)(57,69)(59,71)(60,72)(63,75)(64,76)(66,77)(67,70)(73,78)(74,79);(48,50)(49,54)(51,58)(52,59)(53,60)(55,65)(56,66)(57,67)(61,71)(62,72)(63,73)(64,74)(68,77)(69,70)(75,78)(76,79);(48,49,53,57)(50,54,60,67)(51,55,62,69)(52,63,64,56)(58,70,72,65)(59,73,74,66)(61,75,76,68)(71,77,79,78);(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)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1036304);

D47×#3028 #27083014