Finite Group Databasebeta

← Prev (#72189237) Next (#72189239) →

C4×C9×C11×C27 #72189238

order10692
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 174960
homologyAbelianization (H1) = G · Schur multiplier (H2) = C9

Aliases

abelianC4×C9×C11×C27

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3×C9C2×C32×C11
socle, prime radicalC2×C32×C11C2×C3×C9
LCSG ▷ C1
UCSC1 ◁ G

216 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10692 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC8×C9×C11×C27, C2×C4×C9×C11×C27, C4×C9×C11×C81, …
maximal normal subgroup ofC8×C9×C11×C27, C2×C4×C9×C11×C27, C4×C9×C11×C81, …
maximal quotient ofC8×C9×C11×C27, C2×C4×C9×C11×C27, C4×C9×C11×C81, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.