Finite Group Databasebeta

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C3×#13104711 #72231404

order4800
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24

Aliases

direct productC3×#13104711

Splittings

FittingC3×C52×C22⋊C4 ⋊ C4
HallC3×C52 ⋊ #385
SylowC52 ⋊ C3×#385

Subgroups

subgroupG/H
centerC22×C3C22×#1043
commutatorC22×C52C22×C3×C4
FrattiniC22C22×C3×#1043
FittingC3×C52×C22⋊C4C4
socleC22×C3×C52C22×C4
prime radicalC23×C3×C5⋊D5C22
cosocleC22×C5⋊D5C23×C3
hypercenterC3×C22⋊C4#1043
hypocenterC52C3×#385
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C22×C3 ◁ C3×C22⋊C4

1872 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 600

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.