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Cayley diagram

C3×#4047 #91618

order480
isoclinismisoclinic class of Dic10
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22

Aliases

direct productC3×#4047

Splittings

FittingC2×C3×C5×C8 ⋊ C2
HallC3×C5 ⋊ #131
SylowC5 ⋊ C3×#131

Subgroups

subgroupG/H
centerC3×C8C2×D5
commutatorC2×C5C22×C3×C4
FrattiniC4C22×C3×D5
FittingC2×C3×C5×C8C2
socleC2×C3×C5C22×C4
prime radicalC3×#709C2
cosocleC4×C5C23×C3
hypercenterC2×C3×C8D5
hypocenterC5C3×#131
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C8 ◁ C2×C3×C8

124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 3 generators on 24 points:

(1,2,4,5,3)(6,14,16,8,10,20,9,15)(7,19,18,12,11,21,13,17)(22,23,24);(7,11)(12,17)(13,18)(19,21);(2,3)(4,5)(6,7)(8,12)(9,13)(10,11)(14,19)(15,17)(16,18)(20,21)

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11745885, #11745886, C3×#64728, …
maximal normal subgroup of#11745885, #11745886, C3×#64728, …
maximal quotient ofC3×C8×Dic10, C3×#64968, C3×C8×D20, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 694);