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Cayley diagram

C3×#4147 #92068

order480
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C25

Aliases

direct productC3×#4147

Splittings

FittingC2×C3×C5×Q8 ⋊ C2
HallC3×C5 ⋊ 2−1+4
SylowC5 ⋊ C3×2−1+4

Subgroups

subgroupG/H
centerC2×C3C23×D5
commutator, cosocleC2×C5C24×C3
FrattiniC2C23×C3×D5
FittingC2×C3×C5×Q8C2
socleC2×C3×C5C24
hypercenterC2×C3×Q8D5
hypocenterC5C3×2−1+4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C2×C3×Q8

292 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 generators on 24 points:

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

Conjugacy classes & character table

111 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11749383, #11749384, #11749390, …
maximal normal subgroup of#11749383, #11749384, #11749390, …
maximal quotient ofC3×#65834, C3×#65838, C3×#65841, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1144);