Finite Group Databasebeta

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C22×C3×C7×C8×C9 #72185228

order6048
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 248832
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3

Aliases

abelianC22×C3×C7×C8×C9
multiplicative(ℤ/9417)ˣ, (ℤ/10731)ˣ, (ℤ/12556)ˣ, (ℤ/14308)ˣ, (ℤ/18834)ˣ, (ℤ/21462)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3×C4C23×C32×C7
socle, prime radicalC23×C32×C7C3×C4
LCSG ▷ C1
UCSC1 ◁ G

760 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6048 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C7×C9×C16, C2×C3×C4×C7×C8×C9, C23×C3×C7×C8×C9, …
maximal normal subgroup ofC22×C3×C7×C9×C16, C2×C3×C4×C7×C8×C9, C23×C3×C7×C8×C9, …
maximal quotient ofC22×C3×C7×C9×C16, C2×C3×C4×C7×C8×C9, C23×C3×C7×C8×C9, …
automorphism group ofC3×C43×C73, C3×C49×C73
outer automorphism group ofC3×C43×C73, C3×C49×C73

GAP

Past the SmallGroups library coverage — no SmallGroups id.