Finite Group Databasebeta

← Prev (#65257) Next (#65259) →

C₂×#3942 #65258

order	320
isoclinism	isoclinic class of #686
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

Splittings

C₅ ⋊ C₂×#103

Subgroups

	subgroup	G/H
center	C₂³	C₂²⋊D₅
commutator	C₄×C₅	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₅
Fitting	C₂×C₅×C₄⋊C₄	C₂
socle, prime radical	C₂³×C₅	D₄
cosocle	C₂×C₄×C₅	C₂³
hypercenter	C₂×C₄⋊C₄	D₅
hypocenter	C₅	C₂×#103
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

162 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 320

A minimal faithful permutation representation — 3 generators on 19 points:

(3,4,5,6)(7,8,10,11,9)(13,16)(14,19)(17,18);(8,9)(10,11)(12,13,15,18)(14,16,19,17);(1,2)

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#10599574, #10599576, #10599586, …
maximal normal subgroup of	#10599574, #10599576, #10599586, …
maximal quotient of	C₂×#64672, #10600264, C₄×#3942, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 596);