Finite Group Databasebeta

← Prev (#11756973) Next (#11756975) →

C₃×#66266 #11756974

order	960
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

Splittings

Fitting	C₃×C₅×#41 ⋊ C₄
Hall	C₃×C₅ ⋊ #520
Sylow	C₅ ⋊ C₃×#520

Subgroups

	subgroup	G/H
center	C₂×C₃	C₂³×AGL(1,𝔽₅)
commutator	C₂×C₅	C₂³×C₃×C₄
Frattini	C₂	C₂³×C₃×AGL(1,𝔽₅)
Fitting	C₃×C₅×#41	C₄
socle	C₂×C₃×C₅	C₂³×C₄
prime radical	C₃×D₅×#41	C₂
cosocle	C₂×D₅	C₂⁴×C₃
hypercenter	C₃×#41	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#520
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₃×#41

588 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×#10604003, #14299773, C₃×#10604004, …
maximal normal subgroup of	C₃×#10604003, #14299773, C₃×#10604004, …
maximal quotient of	C₃×#10617127, C₃×#10617172, C₃×#10617208, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 11169);