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C₂×C₃⋊#672 #91095

order	480
isoclinism	isoclinic class of D₁₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₃⋊#672
unambiguous semidirect product	(C₂×C₃)⋊#672

Splittings

derived, Hall	C₃×C₅ ⋊ C₂×C₁₆
Sylow	C₅ ⋊ C₂×C₃⋊C₁₆
Sylow	C₃ ⋊ C₂×#672

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₈	D₁₅
commutator, hypocenter	C₃×C₅	C₂×C₁₆
Frattini	C₈	C₂×D₁₅
Fitting	C₂×C₃×C₅×C₈	C₂
socle, prime radical	C₂²×C₃×C₅	C₈
cosocle	C₃×C₅×C₈	C₂²
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₈

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 2 generators on 26 points:

(1,2)(4,5)(7,8)(9,10)(11,12,13,16,14,17,19,22,15,18,20,23,21,24,25,26);(1,2)(3,4,5)(6,7,9,10,8)

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	Dic₅×C₃⋊C₁₆, Dic₃×#672, #11745873, …
maximal normal subgroup of	Dic₅×C₃⋊C₁₆, Dic₃×#672, #11745873, …
maximal quotient of	C₄×C₃⋊#672, C₄⋊(C₃⋊#672), C₂×C₃⋊#3926, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 171);