Finite Group Databasebeta

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C23×C32×C149 #72189273

order10728
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1193472
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3

Aliases

abelianC23×C32×C149

Subgroups

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

192 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10728 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C32×C4×C149, C24×C32×C149, C23×C3×C9×C149, …
maximal normal subgroup ofC22×C32×C4×C149, C24×C32×C149, C23×C3×C9×C149, …
maximal quotient ofC22×C32×C4×C149, C24×C32×C149, C23×C3×C9×C149, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.