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D₅×#95 #64952

order	320
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂⁵

Aliases

Splittings

Fitting	C₅×#95 ⋊ C₂
Sylow	C₅ ⋊ C₂×#95

Subgroups

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₅
commutator	C₂×C₅	C₂×C₄²
Fitting	C₅×#95	C₂
socle, cosocle	C₂³×C₅	C₂³
prime radical	C₂³×D₅	C₂²
hypercenter	#95	D₅
hypocenter	C₅	C₂×#95
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ #95

330 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:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#10598504, D₅×#327, #10599095, …
maximal normal subgroup of	#10598504, D₅×#327, #10599095, …
maximal quotient of	D₅×#336, #10599453, #10599454, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 290);