Finite Group Databasebeta

← Prev (#91197) Next (#91199) →

C₃×#3994 #91198

order	480
isoclinism	isoclinic class of #3993
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂

Aliases

Splittings

Fitting	C₃×C₅×C₈ ⋊ C₄
Hall	C₃×C₅ ⋊ #107
Sylow	C₅ ⋊ C₃×#107

Subgroups

	subgroup	G/H
center	C₂×C₃	C₄⋊AGL(1,𝔽₅)
commutator	C₄×C₅	C₂×C₃×C₄
Frattini	C₄	C₂×C₃×AGL(1,𝔽₅)
Fitting	C₃×C₅×C₈	C₄
socle	C₂×C₃×C₅	C₄⋊C₄
prime radical	C₂×C₃×D₅	D₄
cosocle	C₄×D₅	C₂²×C₃
hypercenter	C₃×C₈	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#107
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 120

A minimal faithful permutation representation — 2 generators on 16 points:

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

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11746456, #11746458, #11746476, …
maximal normal subgroup of	#11746456, #11746458, #11746476, …
maximal quotient of	C₃×#64849, C₃×#64850, C₃×#64851, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 274);