Finite Group Databasebeta

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C22×C11×C121 #72184643

order5324
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 798600
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C11

Aliases

abelianC22×C11×C121

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC11C22×C112
socle, prime radicalC22×C112C11
LCSG ▷ C1
UCSC1 ◁ G

130 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5324 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C4×C11×C121, C23×C11×C121, C22×C3×C11×C121, …
maximal normal subgroup ofC2×C4×C11×C121, C23×C11×C121, C22×C3×C11×C121, …
maximal quotient ofC2×C4×C11×C121, C23×C11×C121, C22×C3×C11×C121, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.