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C₂×#6663 #91320

order	480
isoclinism	isoclinic class of #6654
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

Splittings

Hall	C₃×C₅ ⋊ C₂×Q₁₆
Sylow	C₅ ⋊ C₂×Dic₁₂
Sylow	C₃ ⋊ C₂×#689

Subgroups

	subgroup	G/H
center	C₂²	#1203
commutator, cosocle	C₃×C₄×C₅	C₂³
Frattini	C₄	C₂×D₃×D₅
Fitting	C₂×C₃×C₄×C₅	C₂²
socle, prime radical	C₂²×C₃×C₅	D₄
hypercenter	C₂×C₄	D₃×D₅
hypocenter	C₃×C₅	C₂×Q₁₆
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 3 generators on 26 points:

(1,2)(4,5)(6,7,9,10,8)(11,13,15,21)(12,16,18,24)(14,22,23,20)(17,25,26,19);(3,4,5)(7,8)(9,10)(11,12,14,17,15,18,23,26)(13,19,20,24,21,25,22,16);(1,2)

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11746884, #11747030, C₄×#6663, …
maximal normal subgroup of	#11746884, #11747030, C₄×#6663, …
maximal quotient of	#11746929, #11746930, #11746955, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 396);