Finite Group Databasebeta

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Cayley diagram

C3×#4011 #91215

order480
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22

Aliases

direct productC3×#4011

Splittings

FittingC23×C3×C5 ⋊ C4
HallC3×C5 ⋊ #99
SylowC5 ⋊ C3×#99

Subgroups

subgroupG/H
centerC2×C3C22⋊AGL(1,𝔽5)
commutatorC22×C5C2×C3×C4
FrattiniC22C2×C3×AGL(1,𝔽5)
FittingC23×C3×C5C4
socleC2×C3×C5C22⋊C4
prime radicalC2×C3×C22⋊D5C2
cosocleC22×D5C22×C3
hypercenterC23×C3AGL(1,𝔽5)
hypocenterC5C3×#99
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C23×C3

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 16
transitive degreeμt(G) = 120

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

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

Conjugacy classes & character table

57 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11746577, #11746579, #11746581, …
maximal normal subgroup of#11746577, #11746579, #11746581, …
maximal quotient ofC3×#64914, C3×#64916, C3×#64917, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 291);