Finite Group Databasebeta

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C82×C9×C11 #72185491

order6336
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 92160
homologyAbelianization (H1) = G · Schur multiplier (H2) = C8

Aliases

abelianC82×C9×C11
multiplicative(ℤ/6497)ˣ, (ℤ/12994)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3×C42C22×C3×C11
socle, prime radicalC22×C3×C11C3×C42
LCSG ▷ C1
UCSC1 ◁ G

222 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6336 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC8×C9×C11×C16, C2×C82×C9×C11, C82×C11×C27, …
maximal normal subgroup ofC8×C9×C11×C16, C2×C82×C9×C11, C82×C11×C27, …
maximal quotient ofC8×C9×C11×C16, C2×C82×C9×C11, C82×C11×C27, …
automorphism group ofC73×C89
outer automorphism group ofC73×C89

GAP

Past the SmallGroups library coverage — no SmallGroups id.