Finite Group Databasebeta

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C23×C3×C7×C8×C9 #72190485

order12096
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 27869184
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26×C3

Aliases

abelianC23×C3×C7×C8×C9
multiplicative(ℤ/25112)ˣ, (ℤ/26144)ˣ, (ℤ/28448)ˣ, (ℤ/28616)ˣ, (ℤ/29792)ˣ, (ℤ/36576)ˣ, (ℤ/37152)ˣ, (ℤ/37668)ˣ, (ℤ/42336)ˣ, (ℤ/42924)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3×C4C24×C32×C7
socle, prime radicalC24×C32×C7C3×C4
LCSG ▷ C1
UCSC1 ◁ G

3380 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12096 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C3×C7×C9×C16, C22×C3×C4×C7×C8×C9, C24×C3×C7×C8×C9
maximal normal subgroup ofC23×C3×C7×C9×C16, C22×C3×C4×C7×C8×C9, C24×C3×C7×C8×C9
maximal quotient ofC23×C3×C7×C9×C16, C22×C3×C4×C7×C8×C9, C24×C3×C7×C8×C9
automorphism group ofC8×C43×C73, C19×C32×C43, C7×C32×C127, …
outer automorphism group ofC8×C43×C73, C19×C32×C43, C7×C32×C127, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.