Finite Group Databasebeta

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C3×#11716609 #72259796

order2400
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2

Aliases

direct productC3×#11716609

Splittings

HallC3×C52 ⋊ #104
SylowC52 ⋊ C3×#104

Subgroups

subgroupG/H
centerC3×C4#6037
commutatorC4×C52C2×C3×C4
FrattiniC2×C4C3×D52
FittingC2×C3×C4×C52C22
socleC2×C3×C52C22⋊C4
prime radicalC3×C5×#709C2
cosocleC2×C4×C52C22×C3
hypercenterC2×C3×C4D52
hypocenterC52C3×#104
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C3×C4 ◁ C2×C3×C4

236 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 68 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

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

Relationships

maximal subgroup ofC3×#13100574, D3×#11716609, #72260143
maximal normal subgroup ofC3×#13100574, D3×#11716609, #72260143

GAP

Past the SmallGroups library coverage — no SmallGroups id.