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C₂²×#1204 #92045

order	480
isoclinism	isoclinic class of #1201
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵

Aliases

Splittings

Hall	C₃×C₅ ⋊ C₂²×Q₈
Sylow	C₅ ⋊ C₂²×Dic₆
Sylow	C₃ ⋊ C₂²×Dic₁₀

Subgroups

	subgroup	G/H
center, hypercenter	C₂³	D₃×D₅
commutator, cosocle	C₂×C₃×C₅	C₂⁴
Frattini	C₂	C₂²×D₃×D₅
Fitting, socle, prime radical	C₂³×C₃×C₅	C₂²
hypocenter	C₃×C₅	C₂²×Q₈
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³

312 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 4 generators on 20 points:

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

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11748567, #11748579, #11748628, …
maximal normal subgroup of	#11748567, #11748579, #11748628, …
maximal quotient of	C₂×#91381, C₂×#91384, C₂×#91388, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1121);