Finite Group Databasebeta

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C3×#13096688 #72254245

order4704
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C25

Aliases

direct productC3×#13096688

Splittings

FittingC2×C3×C4×C72 ⋊ C22
HallC3×C72 ⋊ C2×#41
SylowC72 ⋊ C2×C3×#41

Subgroups

subgroupG/H
centerC3×C4C2×D72
commutator, cosocleC2×C72C24×C3
FrattiniC2C22×C3×D72
FittingC2×C3×C4×C72C22
socleC2×C3×C72C24
hypercenterC2×C3×C4D72
hypocenterC72C2×C3×#41
LCSG ▷ C2×C72 ▷ C72
UCSC1 ◁ C3×C4 ◁ C2×C3×C4

818 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD3×#13096688, C3×#72214319, C3×#72214529, …
maximal normal subgroup ofD3×#13096688, C3×#72214319, C3×#72214529, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.