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D₅×#101 #65039

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

Aliases

Splittings

Fitting	C₅×#101 ⋊ C₂
Sylow	C₅ ⋊ C₂×#101

Subgroups

	subgroup	G/H
center	C₂	D₅×C₂²⋊C₄
commutator	C₂²×C₅	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₅
Fitting	C₅×#101	C₂
socle	C₂×C₅	C₂×C₂²⋊C₄
prime radical	C₂²×D₅	C₂×C₄
cosocle	C₂×C₄×C₅	C₂³
hypercenter	#101	D₅
hypocenter	C₅	C₂×#101
LCS	G ▷ C₂²×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #101

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 80

A minimal faithful permutation representation — 3 generators on 21 points:

(1,2,4,5,3)(6,8,10,16)(7,11,12,14)(9,17,18,15)(13,21,20,19);(6,7,9,13,10,12,18,20)(8,14,15,21,16,11,17,19);(2,3)(4,5)

Conjugacy classes & character table

44 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#10598577, D₅×#355, #10599957, …
maximal normal subgroup of	#10598577, D₅×#355, #10599957, …
maximal quotient of	#10598918, #10598920, #10598921, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 377);