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C₂²×#1220 #92103

order	480
isoclinism	isoclinic class of Dic₃₀
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

Splittings

Fitting	C₂⁴×C₃×C₅ ⋊ C₂
Hall	C₃×C₅ ⋊ C₂²×D₄
Sylow	C₅ ⋊ C₂²×#67
Sylow	C₃ ⋊ C₂²×C₂²⋊D₅

Subgroups

	subgroup	G/H
center	C₂³	C₂×D₁₅
commutator, cosocle	C₂×C₃×C₅	C₂⁴
Frattini	C₂	C₂³×D₁₅
Fitting	C₂⁴×C₃×C₅	C₂
socle	C₂³×C₃×C₅	C₂²
hypercenter	C₂⁴	D₁₅
hypocenter	C₃×C₅	C₂²×D₄
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂⁴

472 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 4 generators on 16 points:

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

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×#90997, #11749483, #11749494, …
maximal normal subgroup of	C₂×#90997, #11749483, #11749494, …
maximal quotient of	C₂²×#6712, C₂×#91813, C₂²×#6714, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1179);