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C₂×#3926 #64718

order	320
isoclinism	isoclinic class of D₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₃₂ · Schur multiplier (H₂) = C₂

Aliases

Splittings

C₅ ⋊ C₂×C₃₂

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₆	D₅
commutator, hypocenter	C₅	C₂×C₃₂
Frattini	C₁₆	C₂×D₅
Fitting	C₂×C₅×C₁₆	C₂
socle, prime radical	C₂²×C₅	C₁₆
cosocle	C₅×C₁₆	C₂²
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₁₆

34 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 320

A minimal faithful permutation representation — 2 generators on 39 points:

(1,2)(4,5)(6,7)(8,9,10,14,11,15,18,24,12,16,19,25,21,27,30,34,13,17,20,26,22,28,31,35,23,29,32,36,33,37,38,39);(1,2)(3,4,6,7,5)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₄×#3926, #10597999, C₄⋊#3926, …
maximal normal subgroup of	C₄×#3926, #10597999, C₄⋊#3926, …
maximal quotient of	C₄×#3926, C₄⋊#3926, C₂×#64663, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 56);