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C₂³×C₅×Dic₃ #92087

order	480
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₅ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂³×C₅×Dic₃

Splittings

derived, Sylow	C₃ ⋊ C₂³×C₄×C₅
Hall	C₃×C₅ ⋊ C₂³×C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂⁴×C₅	D₃
commutator, hypocenter	C₃	C₂³×C₄×C₅
Frattini	C₂	C₂³×C₅×D₃
Fitting, socle, prime radical	C₂⁴×C₃×C₅	C₂
cosocle	C₂×C₃	C₂⁴×C₅
LCS	G ▷ C₃
UCS	C₁ ◁ C₂⁴×C₅

472 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 4 generators on 18 points:

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

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×#90994, #11749472, Dic₃×C₂²⋊Dic₅, …
maximal normal subgroup of	C₂×#90994, #11749472, Dic₃×C₂²⋊Dic₅, …
maximal quotient of	C₂³×C₅×C₃⋊C₈, C₂²×C₅×#208, C₂²×C₄×C₅×Dic₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1163);