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C₂³×Dic₁₅ #92102

order	480
isoclinism	isoclinic class of D₁₅
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂³×Dic₁₅

Splittings

derived, Hall	C₃×C₅ ⋊ C₂³×C₄
Sylow	C₅ ⋊ C₂³×Dic₃
Sylow	C₃ ⋊ C₂³×Dic₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂⁴	D₁₅
commutator, hypocenter	C₃×C₅	C₂³×C₄
Frattini	C₂	C₂³×D₁₅
Fitting, socle, prime radical	C₂⁴×C₃×C₅	C₂
cosocle	C₂×C₃×C₅	C₂⁴
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂⁴

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

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×#90994, #11749473, #11749487, …
maximal normal subgroup of	C₂×#90994, #11749473, #11749487, …
maximal quotient of	C₂³×C₃⋊#168, C₂²×#6710, C₂²×C₄×Dic₁₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1178);