Finite Group Databasebeta

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C23×C32×C11×C13 #72188937

order10296
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 967680
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3

Aliases

abelianC23×C32×C11×C13
multiplicative(ℤ/12719)ˣ, (ℤ/15879)ˣ, (ℤ/16353)ˣ, (ℤ/18039)ˣ, (ℤ/21172)ˣ, (ℤ/24052)ˣ, (ℤ/25438)ˣ, (ℤ/30924)ˣ, (ℤ/31758)ˣ, (ℤ/32706)ˣ, (ℤ/36078)ˣ

Subgroups

subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

384 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10296 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C32×C4×C11×C13, C24×C32×C11×C13, C23×C3×C9×C11×C13, …
maximal normal subgroup ofC22×C32×C4×C11×C13, C24×C32×C11×C13, C23×C3×C9×C11×C13, …
maximal quotient ofC22×C32×C4×C11×C13, C24×C32×C11×C13, C23×C3×C9×C11×C13, …
automorphism group ofC7×C23×C79
outer automorphism group ofC7×C23×C79

GAP

Past the SmallGroups library coverage — no SmallGroups id.