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C₂×#6718 #91832

order	480
isoclinism	isoclinic class of #6715
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

Splittings

Hall	C₃×C₅ ⋊ C₂×Q₁₆
Sylow	C₅ ⋊ C₂×#216
Sylow	C₃ ⋊ C₂×#689

Subgroups

	subgroup	G/H
center	C₂²	#1220
commutator, cosocle	C₃×C₄×C₅	C₂³
Frattini	C₄	C₂²×D₁₅
Fitting	C₂×C₃×C₅×Q₈	C₂
socle, prime radical	C₂²×C₃×C₅	D₄
hypercenter	C₂×Q₈	D₁₅
hypocenter	C₃×C₅	C₂×Q₁₆
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₈

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:

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

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11749244, #11749246, #11749248, …
maximal normal subgroup of	#11749244, #11749246, #11749248, …
maximal quotient of	C₂×#91091, C₂×#91094, #11751071, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 908);