Finite Group Databasebeta

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C33×C5×C82 #72187490

order8640
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 69009408
homologyAbelianization (H1) = G · Schur multiplier (H2) = C33×C8

Aliases

abelianC33×C5×C82

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC42C22×C33×C5
socle, prime radicalC22×C33×C5C42
LCSG ▷ C1
UCSC1 ◁ G

2072 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 ofC33×C5×C8×C16, C2×C33×C5×C82, C32×C5×C82×C9, …
maximal normal subgroup ofC33×C5×C8×C16, C2×C33×C5×C82, C32×C5×C82×C9, …
maximal quotient ofC33×C5×C8×C16, C2×C33×C5×C82, C32×C5×C82×C9, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.