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C₈×Dic₁₅ #91097

order	480
isoclinism	isoclinic class of D₁₅
automorphism	?
homology	Abelianization (H₁) = C₄×C₈ · Schur multiplier (H₂) = C₄

Aliases

C₈×Dic₁₅

Splittings

derived, Hall	C₃×C₅ ⋊ C₄×C₈
Sylow	C₅ ⋊ C₈×Dic₃
Sylow	C₃ ⋊ C₈×Dic₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₈	D₁₅
commutator, hypocenter	C₃×C₅	C₄×C₈
Frattini	C₂×C₄	C₂×D₁₅
Fitting	C₂×C₃×C₅×C₈	C₂
socle, prime radical	C₂²×C₃×C₅	C₂×C₄
cosocle	C₂×C₃×C₄×C₅	C₂²
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂×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)(7,8)(9,10,11,12);(1,2,4,5,3)(6,7,8)(13,14,15,17,16,18,19,20)

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11745872, #11745875, #11745928, …
maximal normal subgroup of	#11745872, #11745875, #11745928, …
maximal quotient of	C₈×C₃⋊#168, #11746275, C₁₆×Dic₁₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 173);