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D₅×#106 #65148

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

Aliases

Splittings

Fitting	C₅×#106 ⋊ C₂
Sylow	C₅ ⋊ C₂×#106

Subgroups

	subgroup	G/H
center	C₂²	D₄×D₅
commutator	C₄×C₅	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₅
Fitting	C₅×#106	C₂
socle	C₂²×C₅	C₂×D₄
prime radical	C₂²×D₅	D₄
cosocle	C₂×C₄×C₅	C₂³
hypercenter	#106	D₅
hypocenter	C₅	C₂×#106
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

130 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:

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

Conjugacy classes & character table

56 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#10598603, #10598605, D₅×#360, …
maximal normal subgroup of	#10598603, #10598605, D₅×#360, …
maximal quotient of	D₅×#334, #10599322, #10599325, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 486);