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C₃×C₈×Dic₅ #91015

order	480
isoclinism	isoclinic class of D₅
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₈ · Schur multiplier (H₂) = C₄

Aliases

C₃×C₈×Dic₅

Splittings

derived, Sylow	C₅ ⋊ C₃×C₄×C₈
Hall	C₃×C₅ ⋊ C₄×C₈

Subgroups

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

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 2 generators on 20 points:

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

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	Dic₅×C₃⋊C₁₆, #11745873, #11745927, …
maximal normal subgroup of	Dic₅×C₃⋊C₁₆, #11745873, #11745927, …
maximal quotient of	C₃×C₈×#168, C₃×#64674, C₃×C₁₆×Dic₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 91);