Finite Group Databasebeta

← Prev (#91013) Next (#91015) →

Cayley diagram

C3×#3944 #91014

order480
isoclinismisoclinic class of Dic10
automorphism?
homologyAbelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C1

Aliases

direct productC3×#3944

Splittings

HallC3×C5 ⋊ M32
SylowC5 ⋊ C3×M32

Subgroups

subgroupG/H
centerC3×C8C2×D5
commutatorC2×C5C2×C3×C8
FrattiniC8C2×C3×D5
FittingC2×C3×C5×C8C2
socleC2×C3×C5C2×C8
prime radicalC22×C3×C5C8
cosocleC5×C8C22×C3
hypercenterC2×C3×C8D5
hypocenterC5C3×M32
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C8 ◁ C2×C3×C8

52 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)(7,11)(12,17)(13,18)(19,21)(22,23,24);(2,3)(4,5)(6,12,14,11,16,21,8,13,10,17,20,7,9,19,15,18)

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11745877, #11745878, #11745883, …
maximal normal subgroup of#11745877, #11745878, #11745883, …
maximal quotient ofC3×#64681, C3×C4⋊#672, C3×C22⋊#672, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 90);