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D₃×Dic₂₀ #91262

order	480
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

D₃×Dic₂₀

Splittings

Hall	C₃×C₅ ⋊ C₂×Q₁₆
Sylow	C₅ ⋊ D₃×Q₁₆
Sylow	C₃ ⋊ C₂×Dic₂₀

Subgroups

	subgroup	G/H
center	C₂	D₃×D₂₀
commutator, cosocle	C₃×C₄×C₅	C₂³
Frattini	C₄	C₂×D₃×D₅
Fitting	C₃×C₅×C₈	C₂²
socle	C₂×C₃×C₅	C₂×D₄
prime radical	C₂×C₅×D₃	D₄
hypercenter	C₈	D₃×D₅
hypocenter	C₃×C₅	C₂×Q₁₆
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 3 generators on 24 points:

(1,2,4,5,3)(6,8,15,19,10,17,9,16)(7,11,18,21,13,20,12,14)(22,23,24);(2,3)(4,5)(6,7,10,13)(8,14,17,21)(9,18,15,12)(11,19,20,16);(23,24)

Conjugacy classes & character table

69 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#3932, D₃×Dic₄₀, #11746830, …
maximal normal subgroup of	D₃×#3932, D₃×Dic₄₀, #11746830, …
maximal quotient of	D₃×#3948, D₃×#3950, #11747629, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 338);