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C₂×#3965 #65505

order	320
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

Splittings

C₅ ⋊ C₂×#100

Subgroups

	subgroup	G/H
center	C₂²	C₂²⋊Dic₅
commutator	C₂²×C₅	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₅
Fitting, prime radical	C₂²×C₅×D₄	C₂
socle	C₂²×C₅	C₂²⋊C₄
cosocle	C₂×C₄×C₅	C₂³
hypercenter	C₂²×D₄	D₅
hypocenter	C₅	C₂×#100
LCS	G ▷ C₂²×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×D₄

186 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 80

A minimal faithful permutation representation — 3 generators on 15 points:

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

Conjugacy classes & character table

62 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#10598128, #10598185, #10600435, …
maximal normal subgroup of	#10598128, #10598185, #10600435, …
maximal quotient of	C₂×#64745, #10602332, C₂×#64750, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 843);