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Cayley diagram

C3×#3993 #91197

order480
isoclinismisoclinic class of #3993
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2

Aliases

direct productC3×#3993

Splittings

FittingC3×C5×C8 ⋊ C4
HallC3×C5 ⋊ #106
SylowC5 ⋊ C3×#106

Subgroups

subgroupG/H
centerC2×C3C4⋊AGL(1,𝔽5)
commutatorC4×C5C2×C3×C4
FrattiniC4C2×C3×AGL(1,𝔽5)
FittingC3×C5×C8C4
socleC2×C3×C5C4⋊C4
prime radicalC2×C3×D5D4
cosocleC4×D5C22×C3
hypercenterC3×C8AGL(1,𝔽5)
hypocenterC5C3×#106
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×C8

72 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)(6,10,12,7,9,13,8,11)(14,15,16);(2,5,4,3)(7,10)(8,12)(11,13)

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11746464, #11746465, #11746472, …
maximal normal subgroup of#11746464, #11746465, #11746472, …
maximal quotient ofC3×#64847, C3×ΓL(1,𝔽81), C3×#64881, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 273);