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Cayley diagram

C3×#3961 #91031

order480
isoclinismisoclinic class of #3958
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×#3961

Splittings

HallC3×C5 ⋊ Q32
SylowC5 ⋊ C3×Q32

Subgroups

subgroupG/H
centerC2×C3#686
commutator, cosocleC5×C8C22×C3
FrattiniC8C2×C3×D5
FittingC3×C5×Q16C2
socle, prime radicalC2×C3×C5D8
hypercenterC3×Q16D5
hypocenterC5C3×Q32
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×C8 ◁ C3×Q16

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:

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

Conjugacy classes & character table

75 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#3961, #11748297, #11748298, …
maximal normal subgroup ofD3×#3961, #11748297, #11748298, …
maximal quotient ofC3×#64709, C3×#64712, C3×#64784, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 107);