Finite Group Databasebeta

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C33×C5×C8×C9 #72188409

order9720
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 786060288
homologyAbelianization (H1) = G · Schur multiplier (H2) = C36

Aliases

abelianC33×C5×C8×C9

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3×C4C2×C34×C5
socle, prime radicalC2×C34×C5C3×C4
LCSG ▷ C1
UCSC1 ◁ G

3168 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9720 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC33×C5×C9×C16, C2×C33×C5×C8×C9, C33×C5×C8×C27, …
maximal normal subgroup ofC33×C5×C9×C16, C2×C33×C5×C8×C9, C33×C5×C8×C27, …
maximal quotient ofC33×C5×C9×C16, C2×C33×C5×C8×C9, C33×C5×C8×C27, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.