Finite Group Databasebeta

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Cayley diagram

C3×#4013 #91217

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

Aliases

direct productC3×#4013

Splittings

HallC3×C5 ⋊ #100
SylowC5 ⋊ C3×#100

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
cosocleC2×Dic5C22×C3
hypercenterC23×C3AGL(1,𝔽5)
hypocenterC5C3×#100
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C23×C3

92 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)(7,10)(8,12)(14,15,16);(2,5,4,3)(6,11,12,7,9,13,8,10)

Conjugacy classes & character table

57 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11746578, #11746580, #11746582, …
maximal normal subgroup of#11746578, #11746580, #11746582, …
maximal quotient ofC3×#64915, C3×#64919, C3×#64921, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 293);