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C₂×#3963 #65497

order	320
isoclinism	isoclinic class of Dic₁₀
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂⁵

Aliases

Splittings

C₅ ⋊ C₂×#95

Subgroups

	subgroup	G/H
center	C₂⁴	C₂×D₅
commutator	C₂×C₅	C₂×C₄²
Frattini	C₂³	C₂²×D₅
Fitting	C₂³×C₄×C₅	C₂
socle, prime radical	C₂⁴×C₅	C₂²
cosocle	C₂³×C₅	C₂³
hypercenter	C₂³×C₄	D₅
hypocenter	C₅	C₂×#95
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄

330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 320

A minimal faithful permutation representation — 3 generators on 19 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#10598115, #10598165, #10598166, …
maximal normal subgroup of	#10598115, #10598165, #10598166, …
maximal quotient of	C₂×#64743, C₂×#64744, #10602320, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 835);