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D₅×Dic₁₂ #91259

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

Aliases

D₅×Dic₁₂

Splittings

Hall	C₃×C₅ ⋊ C₂×Q₁₆
Sylow	C₅ ⋊ C₂×Dic₁₂
Sylow	C₃ ⋊ D₅×Q₁₆

Subgroups

	subgroup	G/H
center	C₂	D₅×D₁₂
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×C₃×D₅	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:

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

Conjugacy classes & character table

60 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11746458, #11746459, #11746470, …
maximal normal subgroup of	#11746458, #11746459, #11746470, …
maximal quotient of	D₅×#816, D₅×#818, #11747620, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 335);