Finite Group Databasebeta

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C23×C3×C243 #72185083

order5832
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 489888
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3

Aliases

abelianC23×C3×C243
multiplicative(ℤ/10227)ˣ, (ℤ/13636)ˣ, (ℤ/17532)ˣ, (ℤ/20412)ˣ, (ℤ/20454)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC81C23×C32
socle, prime radicalC23×C32C81
LCSG ▷ C1
UCSC1 ◁ G

352 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5832 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C4×C243, C24×C3×C243, C23×C3×C729, …
maximal normal subgroup ofC22×C3×C4×C243, C24×C3×C243, C23×C3×C729, …
maximal quotient ofC22×C3×C4×C243, C24×C3×C243, C23×C3×C729, …
automorphism group ofC3×C7×C487, C4×C7×C729
outer automorphism group ofC3×C7×C487, C4×C7×C729

GAP

Past the SmallGroups library coverage — no SmallGroups id.