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Cayley diagram

C3×#3968 #91038

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

Aliases

direct productC3×#3968

Splittings

HallC3×C5 ⋊ #101
SylowC5 ⋊ C3×#101

Subgroups

subgroupG/H
centerC2×C3C22⋊Dic5
commutatorC22×C5C2×C3×C4
FrattiniC2×C4C2×C3×D5
FittingC2×C3×C5×Q8C2
socleC2×C3×C5C22⋊C4
prime radicalC22×C3×C5C2×C4
cosocleC2×C4×C5C22×C3
hypercenterC2×C3×Q8D5
hypocenterC5C3×#101
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×Q8

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 generators on 24 points:

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

Conjugacy classes & character table

93 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11746013, #11746014, #11746016, …
maximal normal subgroup of#11746013, #11746014, #11746016, …
maximal quotient ofC3×#64748, C3×#64750, C3×#64763, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 114);