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C₄×C₃⋊#168 #91086

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

Aliases

C₄×C₃⋊#168

Splittings

derived, Hall	C₃×C₅ ⋊ C₄×C₈
Sylow	C₅ ⋊ C₄×C₃⋊C₈
Sylow	C₃ ⋊ C₄×#168

Subgroups

	subgroup	G/H
center, hypercenter	C₄²	D₁₅
commutator, hypocenter	C₃×C₅	C₄×C₈
Frattini	C₂×C₄	C₂×D₁₅
Fitting	C₃×C₄²×C₅	C₂
socle, prime radical	C₂²×C₃×C₅	C₂×C₄
cosocle	C₂×C₃×C₄×C₅	C₂²
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₄²

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

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃⋊C₈×#168, #11745831, #11745832, …
maximal normal subgroup of	C₃⋊C₈×#168, #11745831, #11745832, …
maximal quotient of	C₈×C₃⋊#168, #11746276, C₄×C₃⋊#672, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 162);