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C₂³×Dic₁₀ #66270

order	320
isoclinism	isoclinic class of Dic₁₀
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁹

Aliases

C₂³×Dic₁₀

Splittings

C₅ ⋊ C₂³×Q₈

Subgroups

	subgroup	G/H
center	C₂⁴	C₂×D₅
commutator, cosocle	C₂×C₅	C₂⁵
Frattini	C₂	C₂⁴×D₅
Fitting	C₂³×C₄×C₅	C₂
socle, prime radical	C₂⁴×C₅	C₂²
hypercenter	C₂³×C₄	D₅
hypocenter	C₅	C₂³×Q₈
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄

850 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 5 generators on 19 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#10600217, #10600318, #10600756, …
maximal normal subgroup of	#10600217, #10600318, #10600756, …
maximal quotient of	C₂²×C₄×Dic₁₀, C₂²×#4016, C₂²×#4015, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 1608);