Finite Group Databasebeta

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C23×C3×C72×C9 #72189174

order10584
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 36578304
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3×C7

Aliases

abelianC23×C3×C72×C9
multiplicative(ℤ/16383)ˣ, (ℤ/18669)ˣ, (ℤ/21844)ˣ, (ℤ/24892)ˣ, (ℤ/32766)ˣ, (ℤ/37338)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3C23×C32×C72
socle, prime radicalC23×C32×C72C3
LCSG ▷ C1
UCSC1 ◁ G

1600 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10584 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C4×C72×C9, C24×C3×C72×C9, C23×C3×C72×C27, …
maximal normal subgroup ofC22×C3×C4×C72×C9, C24×C3×C72×C9, C23×C3×C72×C27, …
maximal quotient ofC22×C3×C4×C72×C9, C24×C3×C72×C9, C23×C3×C72×C27, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.