Finite Group Databasebeta

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C3×#10705268 #72214462

order2304
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22

Aliases

direct productC3×#10705268

Splittings

FittingC32×#1455 ⋊ C2
SylowC32 ⋊ #11669

Subgroups

subgroupG/H
centerC3×C4#5131
commutatorC2×C3×C8C22×C3×C4
FrattiniC4×C8C22×C3×D3
FittingC32×#1455C2
socleC2×C32#1490
prime radicalC3×#5748C4
cosocleC3×C4×C8C23×C3
hypercenterC3×#1455D3
hypocenterC3C3×#11669
LCSG ▷ C2×C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C4 ◁ C2×C3×C8 ◁ C3×C4×M16 ◁ C3×#1455

827 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup of#72219771, C3×#72215247, #72219779
maximal normal subgroup of#72219771, C3×#72215247, #72219779

GAP

Past the SmallGroups library coverage — no SmallGroups id.