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C₂×C₅×#216 #91746

order	480
isoclinism	isoclinic class of #213
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂²

Aliases

C₂×C₅×#216

Splittings

Hall	C₃×C₅ ⋊ C₂×Q₁₆
Sylow	C₃ ⋊ C₂×C₅×Q₁₆

Subgroups

	subgroup	G/H
center	C₂²×C₅	#67
commutator, cosocle	C₃×C₄	C₂³×C₅
Frattini	C₄	C₂²×C₅×D₃
Fitting	C₂×C₃×C₅×Q₈	C₂
socle, prime radical	C₂²×C₃×C₅	D₄
hypercenter	C₂×C₅×Q₈	D₃
hypocenter	C₃	C₂×C₅×Q₁₆
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅ ◁ C₂×C₅×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)(6,7,8,9,10)(11,13,15,21)(12,16,18,25)(14,23,24,20)(17,26,22,19);(4,5)(11,12,15,18)(13,19,21,26)(14,22,24,17)(16,23,25,20);(1,2)

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	Dic₅×#216, #11749245, #11749247, …
maximal normal subgroup of	Dic₅×#216, #11749245, #11749247, …
maximal quotient of	C₂×C₅×#807, C₂×C₅×#810, C₅×#4970, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 822);