Finite Group Databasebeta

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C22×C3×C9×C83 #72187779

order8964
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 53136
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C3

Aliases

abelianC22×C3×C9×C83
multiplicative(ℤ/9481)ˣ, (ℤ/13473)ˣ, (ℤ/18962)ˣ, (ℤ/26946)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3C22×C32×C83
socle, prime radicalC22×C32×C83C3
LCSG ▷ C1
UCSC1 ◁ G

100 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8964 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C4×C9×C83, C23×C3×C9×C83, C22×C3×C27×C83, …
maximal normal subgroup ofC2×C3×C4×C9×C83, C23×C3×C9×C83, C22×C3×C27×C83, …
maximal quotient ofC2×C3×C4×C9×C83, C23×C3×C9×C83, C22×C3×C27×C83, …
automorphism group ofC19×C499, C2×C27×C499
outer automorphism group ofC19×C499, C2×C27×C499

GAP

Past the SmallGroups library coverage — no SmallGroups id.