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C₂×Dic₃×Dic₅ #91527

order	480
isoclinism	isoclinic class of D₃×D₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂²×C₄

Aliases

C₂×Dic₃×Dic₅

Splittings

derived, Hall	C₃×C₅ ⋊ C₂×C₄²
Sylow	C₅ ⋊ C₂×C₄×Dic₃
Sylow	C₃ ⋊ C₂×C₄×Dic₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂³	D₃×D₅
commutator, hypocenter	C₃×C₅	C₂×C₄²
Frattini	C₂²	C₂×D₃×D₅
Fitting, socle, prime radical	C₂³×C₃×C₅	C₂²
cosocle	C₂²×C₃×C₅	C₂³
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂³

216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 18 points:

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

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11746570, #11748627, #11748628, …
maximal normal subgroup of	#11746570, #11748627, #11748628, …
maximal quotient of	C₂×Dic₅×C₃⋊C₈, Dic₅×#208, #11748318, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 603);