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C₂×C₃×#672 #91013

order	480
isoclinism	isoclinic class of D₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₆ · Schur multiplier (H₂) = C₂

Aliases

C₂×C₃×#672

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₈	D₅
commutator, hypocenter	C₅	C₂×C₃×C₁₆
Frattini	C₈	C₂×C₃×D₅
Fitting	C₂×C₃×C₅×C₈	C₂
socle, prime radical	C₂²×C₃×C₅	C₈
cosocle	C₅×C₈	C₂²×C₃
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₃×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)(3,4,5)(7,8)(9,10)(11,12,13,16,14,17,19,22,15,18,20,23,21,24,25,26);(1,2)(6,7,9,10,8)

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	Dic₃×#672, #11745872, #11745874, …
maximal normal subgroup of	Dic₃×#672, #11745872, #11745874, …
maximal quotient of	C₃×C₄×#672, C₃×C₄⋊#672, C₂×C₃×#3926, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 89);