Finite Group Databasebeta

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C3×#64674 #11746031

order960
isoclinismisoclinic class of Dic10
automorphism?
homologyAbelianization (H1) = C3×C4×C8 · Schur multiplier (H2) = C4

Aliases

direct productC3×#64674

Splittings

HallC3×C5 ⋊ #322
SylowC5 ⋊ C3×#322

Subgroups

subgroupG/H
centerC3×C42C2×D5
commutatorC2×C5C3×C4×C8
FrattiniC42C2×C3×D5
FittingC3×C4×C5×C8C2
socle, prime radicalC22×C3×C5C42
cosocleC42×C5C22×C3
hypercenterC3×C4×C8D5
hypocenterC5C3×#322
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C42 ◁ C3×C4×C8

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 960

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

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

Conjugacy classes & character table

312 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×#10598515, #14277499, C3×D5×#322, …
maximal normal subgroup ofC3×#10598515, #14277499, C3×D5×#322, …
maximal quotient ofC3×#10598144, C3×#10597990, C3×#10597933, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 226);