Finite Group Databasebeta

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C33×C5×C7×C9 #72187382

order8505
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1179090432
homologyAbelianization (H1) = G · Schur multiplier (H2) = C36

Aliases

abelianC33×C5×C7×C9

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3C34×C5×C7
socle, prime radicalC34×C5×C7C3
LCSG ▷ C1
UCSC1 ◁ G

1584 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8505 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C33×C5×C7×C9, C33×C5×C7×C27, C32×C5×C7×C92, …
maximal normal subgroup ofC2×C33×C5×C7×C9, C33×C5×C7×C27, C32×C5×C7×C92, …
maximal quotient ofC2×C33×C5×C7×C9, C33×C5×C7×C27, C32×C5×C7×C92, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.