Finite Group Databasebeta

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C3×#72229453 #72260029

order7200
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22

Aliases

direct productC3×#72229453

Splittings

HallC32×C52 ⋊ C2×M16
SylowC52 ⋊ C2×C3×#208
SylowC32 ⋊ #11716936

Subgroups

subgroupG/H
centerC3×C4C2×D15⋊D5
commutatorC2×C3×C52C22×C3×C4
FrattiniC4C2×C3×D15⋊D5
FittingC2×C32×C4×C52C22
socleC2×C32×C52C22×C4
prime radicalC22×C32×C5⋊D5C4
cosocleC3×C4×C52C23×C3
hypercenterC2×C3×C4D15⋊D5
hypocenterC3×C52C2×C3×M16
LCSG ▷ C2×C3×C52 ▷ C3×C52
UCSC1 ◁ C3×C4 ◁ C2×C3×C4

976 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

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

Relationships

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.