Finite Group Databasebeta

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C22×C29×C81 #72188154

order9396
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 9072
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC22×C29×C81
multiplicative(ℤ/9617)ˣ, (ℤ/14337)ˣ, (ℤ/19234)ˣ, (ℤ/28674)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC27C22×C3×C29
socle, prime radicalC22×C3×C29C27
LCSG ▷ C1
UCSC1 ◁ G

50 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9396 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C4×C29×C81, C23×C29×C81, C22×C29×C243, …
maximal normal subgroup ofC2×C4×C29×C81, C23×C29×C81, C22×C29×C243, …
maximal quotient ofC2×C4×C29×C81, C23×C29×C81, C22×C29×C243, …
automorphism group ofC59×C163, C2×C59×C243
outer automorphism group ofC59×C163, C2×C59×C243

GAP

Past the SmallGroups library coverage — no SmallGroups id.