Finite Group Databasebeta

← Prev (#72253547) Next (#72253549) →

C3×#111458 #72253548

order1536
nilpotency class3
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C28

Aliases

direct productC3×#111458

Subgroups

subgroupG/H
center, socleC23×C3#392
commutatorC25C22×C3×C4
Frattini, cosocleC26C23×C3
prime radicalC2×C3×#2403C2
LCSG ▷ C25 ▷ C22 ▷ C1
UCSC1 ◁ C23×C3 ◁ C26×C3 ◁ G

7768 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

Fitting subgroup ofD3×#111458, #72270070, #72271058
maximal subgroup ofC3×#72219165, D3×#111458, #72270070, …
maximal normal subgroup ofC3×#72219165, D3×#111458, #72270070, …
maximal quotient ofC3×#72219163, C3×#72218521, C3×#72219162

GAP

Past the SmallGroups library coverage — no SmallGroups id.