Finite Group Databasebeta

← Prev (#72260033) Next (#72260035) →

C3×#72229663 #72260034

order7200
automorphism?
homologyAbelianization (H1) = C3×C42 · Schur multiplier (H2) = C2

Aliases

direct productC3×#72229663

Splittings

HallC32×C52 ⋊ #97
SylowC52 ⋊ C3×#803
SylowC32 ⋊ #11716763

Subgroups

subgroupG/H
center, hypercenterC3×C4#10597182
commutatorC2×C3×C52C3×C42
FrattiniC4C3×#10597182
FittingC32×C4×C52C2×C4
socleC2×C32×C52C42
prime radicalC2×C32×C5⋊D5C2×C4
cosocleC3×C4×C5⋊D5C22×C3
hypocenterC3×C52C3×#97
LCSG ▷ C2×C3×C52 ▷ C3×C52
UCSC1 ◁ C3×C4

560 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#72230506
maximal normal subgroup ofC3×#72230506

GAP

Past the SmallGroups library coverage — no SmallGroups id.