Finite Group Databasebeta

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C3×#13099900 #72259832

order4800
automorphism?
homologyAbelianization (H1) = C3×C42 · Schur multiplier (H2) = C22

Aliases

direct productC3×#13099900

Splittings

HallC3×C52 ⋊ #339
SylowC52 ⋊ C3×#339

Subgroups

subgroupG/H
centerC3×C4#87831
commutatorC4×C52C3×C42
FrattiniC2×C4C3×D5⋊AGL(1,𝔽5)
FittingC2×C3×C4×C52C2×C4
socleC2×C3×C52#95
prime radicalC22×C3×C5⋊D5D4
cosocleC2×C4×C5⋊D5C22×C3
hypercenterC2×C3×C4D5⋊AGL(1,𝔽5)
hypocenterC52C3×#339
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C3×C4 ◁ C2×C3×C4

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

normal subgroups only

This group has 656 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

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#72213321
maximal normal subgroup ofC3×#72213321

GAP

Past the SmallGroups library coverage — no SmallGroups id.