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Cayley diagram

C3×#3955 #91025

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

Aliases

direct productC3×#3955

Splittings

FittingC3×C5×M16 ⋊ C2
HallC3×C5 ⋊ #100
SylowC5 ⋊ C3×#100

Subgroups

subgroupG/H
centerC2×C3#685
commutatorC22×C5C2×C3×C4
FrattiniC2×C4C2×C3×D5
FittingC3×C5×M16C2
socleC2×C3×C5C22⋊C4
prime radicalC2×C3×D20C2
cosocleC2×C4×C5C22×C3
hypercenterC3×M16D5
hypocenterC5C3×#100
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×M16

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:

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

Conjugacy classes & character table

93 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11748194, #11748195, #11748196, …
maximal normal subgroup of#11748194, #11748195, #11748196, …
maximal quotient ofC3×#64684, C3×#64688, C3×#64701, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 101);