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C₂²×D₃×Dic₅ #92039

order	480
isoclinism	isoclinic class of D₃×D₅
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂²×D₃×Dic₅

Splittings

derived, Hall	C₃×C₅ ⋊ C₂³×C₄
Sylow	C₅ ⋊ C₂²×C₄×D₃
Sylow	C₃ ⋊ C₂³×Dic₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂³	D₃×D₅
commutator, hypocenter	C₃×C₅	C₂³×C₄
Frattini	C₂	C₂²×D₃×D₅
Fitting, socle	C₂³×C₃×C₅	C₂²
prime radical	C₂³×C₅×D₃	C₂
cosocle	C₂×C₃×C₅	C₂⁴
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂³

472 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 4 generators on 16 points:

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

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	Dic₅×(C₂×D₃)⋊C₄, #11748874, D₃×#3963, …
maximal normal subgroup of	Dic₅×(C₂×D₃)⋊C₄, #11748874, D₃×#3963, …
maximal quotient of	C₂²×D₃×#168, C₂×#91286, C₂×D₃×#681, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1115);