Finite Group Databasebeta

← Prev (#91001) Next (#91003) →

C₃×#3932 #91002

order	480
isoclinism	isoclinic class of D₈₀
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₁

Aliases

Splittings

Fitting	C₃×C₅×C₁₆ ⋊ C₂
Hall	C₃×C₅ ⋊ SD₃₂
Sylow	C₅ ⋊ C₃×SD₃₂

Subgroups

	subgroup	G/H
center	C₂×C₃	D₄₀
commutator, cosocle	C₅×C₈	C₂²×C₃
Frattini	C₈	C₂×C₃×D₅
Fitting	C₃×C₅×C₁₆	C₂
socle	C₂×C₃×C₅	D₈
prime radical	C₃×D₄₀	C₂
hypercenter	C₃×C₁₆	D₅
hypocenter	C₅	C₃×SD₃₂
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈ ◁ C₃×C₁₆

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:

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

Conjugacy classes & character table

129 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#3932, #11746821, #11746823, …
maximal normal subgroup of	D₃×#3932, #11746821, #11746823, …
maximal quotient of	C₃×#64723, C₃×#64725, C₃×#64729, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 78);