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D₈×Dic₅ #65438

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

Aliases

D₈×Dic₅

Splittings

C₅ ⋊ C₄×D₈

Subgroups

	subgroup	G/H
center	C₂²	D₄×D₅
commutator	C₄×C₅	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₅
Fitting, prime radical	C₂×C₅×D₈	C₂
socle	C₂²×C₅	C₂×D₄
cosocle	C₂×C₄×C₅	C₂³
hypercenter	C₂×D₈	D₅
hypocenter	C₅	C₄×D₈
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₈

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 160

A minimal faithful permutation representation — 3 generators on 17 points:

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

Conjugacy classes & character table

56 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#10598799, #10598801, #10599967, …
maximal normal subgroup of	#10598799, #10598801, #10599967, …
maximal quotient of	Dic₅×#102, #10600948, #10600961, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 776);