Finite Group Databasebeta

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C3×C5×C82×C9 #72187489

order8640
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 663552
homologyAbelianization (H1) = G · Schur multiplier (H2) = C3×C8

Aliases

abelianC3×C5×C82×C9

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3×C42C22×C32×C5
socle, prime radicalC22×C32×C5C3×C42
LCSG ▷ C1
UCSC1 ◁ G

740 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8640 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×C8×C9×C16, C2×C3×C5×C82×C9, C3×C5×C82×C27, …
maximal normal subgroup ofC3×C5×C8×C9×C16, C2×C3×C5×C82×C9, C3×C5×C82×C27, …
maximal quotient ofC3×C5×C8×C9×C16, C2×C3×C5×C82×C9, C3×C5×C82×C27, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.