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Cayley diagram

C3×Dic40 #91003

order480
isoclinismisoclinic class of D80
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic40

Splittings

HallC3×C5 ⋊ Q32
SylowC5 ⋊ C3×Q32

Subgroups

subgroupG/H
centerC2×C3D40
commutator, cosocleC5×C8C22×C3
FrattiniC8C2×C3×D5
FittingC3×C5×C16C2
socle, prime radicalC2×C3×C5D8
hypercenterC3×C16D5
hypocenterC5C3×Q32
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×C8 ◁ C3×C16

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 2 generators on 40 points:

(1,2,3)(4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21)(36,37,38,39,40);(4,20,12,28)(5,21,13,29)(6,22,14,30)(7,23,15,31)(8,24,16,32)(9,25,17,33)(10,26,18,34)(11,27,19,35)(37,40)(38,39)

Conjugacy classes & character table

129 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11745822, #11745824, #11745827, …
maximal normal subgroup of#11745822, #11745824, #11745827, …
maximal quotient ofC3×#64723, C3×#64724, C2×C3×Dic40, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 79);