Finite Group Databasebeta

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C23×C33×C72 #72189176

order10584
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 3804143616
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C33×C7

Aliases

abelianC23×C33×C72
multiplicative(ℤ/18963)ˣ, (ℤ/37926)ˣ

Subgroups

subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

4480 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×C33×C4×C72, C24×C33×C72, C23×C32×C72×C9, …
maximal normal subgroup ofC22×C33×C4×C72, C24×C33×C72, C23×C32×C72×C9, …
maximal quotient ofC22×C33×C4×C72, C24×C33×C72, C23×C32×C72×C9, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.