Finite Group Databasebeta

← Prev (#72248560) Next (#72248562) →

C3×#201664 #72248561

order1536
nilpotency class3
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C28

Aliases

direct productC3×#201664

Subgroups

subgroupG/H
center, socleC22×C3C2×#386
commutatorC24C23×C3×C4
Frattini, cosocleC25C24×C3
prime radicalC2×C3×#2403C2
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C3 ◁ C26×C3 ◁ G

7936 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

222 conjugacy classes — view the full character table.

Relationships

Fitting subgroup ofD3×#201664, #72248860, #72255094, …
maximal subgroup ofD3×#201664, #72248860, C3×#72210600, …
maximal normal subgroup ofD3×#201664, #72248860, C3×#72210600, …
maximal quotient ofC3×#72210479, C3×#72213489

GAP

Past the SmallGroups library coverage — no SmallGroups id.