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C₂×D₅⋊(C₃⋊C₈) #91984

order	480
isoclinism	isoclinic class of ΓL(1,𝔽₁₆)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³

Aliases

direct product	C₂×D₅⋊(C₃⋊C₈)
unambiguous semidirect product	D₅⋊(C₂×C₃⋊C₈)

Splittings

derived, Hall	C₃×C₅ ⋊ C₂²×C₈
Sylow	C₅ ⋊ C₂²×C₃⋊C₈
Sylow	C₃ ⋊ C₂×D₅⋊C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₄	ΓL(1,𝔽₁₆)
commutator, hypocenter	C₃×C₅	C₂²×C₈
Frattini	C₂	C₂²×ΓL(1,𝔽₁₆)
Fitting	C₂×C₃×C₄×C₅	C₄
socle	C₂²×C₃×C₅	C₂×C₄
prime radical	C₂²×C₃×D₅	C₄
cosocle	C₃×Dic₅	C₂³
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 240

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

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

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	(C₂×AGL(1,𝔽₅))⋊(C₃⋊C₈), #11746528, #11746531, …
maximal normal subgroup of	(C₂×AGL(1,𝔽₅))⋊(C₃⋊C₈), #11746528, #11746531, …
maximal quotient of	C₄×D₅⋊(C₃⋊C₈), #11752337, D₅⋊(C₄⋊(C₃⋊C₈)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1060);