Finite Group Databasebeta

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Cayley diagram

C3×#3956 #91026

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

Aliases

direct productC3×#3956

Splittings

HallC3×C5 ⋊ #101
SylowC5 ⋊ C3×#101

Subgroups

subgroupG/H
centerC2×C3#685
commutatorC22×C5C2×C3×C4
FrattiniC2×C4C2×C3×D5
FittingC3×C5×M16C2
socleC2×C3×C5C22⋊C4
prime radicalC22×C3×C5C2×C4
cosocleC2×C4×C5C22×C3
hypercenterC3×M16D5
hypocenterC5C3×#101
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×M16

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 2 generators on 24 points:

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

Conjugacy classes & character table

93 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11748197, #11748199, #11748200, …
maximal normal subgroup of#11748197, #11748199, #11748200, …
maximal quotient ofC3×#64685, C3×#64689, C3×#64702, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 102);