Finite Group Databasebeta

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C22×C9×C11×C27 #72189245

order10692
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 524880
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C9

Aliases

abelianC22×C9×C11×C27
multiplicative(ℤ/16119)ˣ, (ℤ/32238)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3×C9C22×C32×C11
socle, prime radicalC22×C32×C11C3×C9
LCSG ▷ C1
UCSC1 ◁ G

360 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 ofC2×C4×C9×C11×C27, C23×C9×C11×C27, C22×C9×C11×C81, …
maximal normal subgroup ofC2×C4×C9×C11×C27, C23×C9×C11×C27, C22×C9×C11×C81, …
maximal quotient ofC2×C4×C9×C11×C27, C23×C9×C11×C27, C22×C9×C11×C81, …
automorphism group ofC2×C81×C199
outer automorphism group ofC2×C81×C199

GAP

Past the SmallGroups library coverage — no SmallGroups id.