Finite Group Databasebeta

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C23×C33×C49 #72189175

order10584
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 79252992
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C33

Aliases

abelianC23×C33×C49

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC7C23×C33×C7
socle, prime radicalC23×C33×C7C7
LCSG ▷ C1
UCSC1 ◁ G

1344 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×C49, C24×C33×C49, C23×C32×C9×C49, …
maximal normal subgroup ofC22×C33×C4×C49, C24×C33×C49, C23×C32×C9×C49, …
maximal quotient ofC22×C33×C4×C49, C24×C33×C49, C23×C32×C9×C49, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.