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C₅×#828 #91071

order	480
isoclinism	isoclinic class of #826
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₁

Aliases

Splittings

Fitting	C₃×C₅×Q₁₆ ⋊ C₂
Hall	C₃×C₅ ⋊ SD₃₂
Sylow	C₃ ⋊ C₅×SD₃₂

Subgroups

	subgroup	G/H
center	C₂×C₅	#213
commutator, cosocle	C₃×C₈	C₂²×C₅
Frattini	C₈	C₂×C₅×D₃
Fitting	C₃×C₅×Q₁₆	C₂
socle	C₂×C₃×C₅	D₈
prime radical	C₅×D₂₄	C₂
hypercenter	C₅×Q₁₆	D₃
hypocenter	C₃	C₅×SD₃₂
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×C₈ ◁ C₅×Q₁₆

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 2 generators on 24 points:

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

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₅×#828, #11748289, #11748292, …
maximal normal subgroup of	D₅×#828, #11748289, #11748292, …
maximal quotient of	C₅×#4490, C₅×#4491, C₅×#4564, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 147);