Finite Group Databasebeta

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C23×C32×C7×C13 #72185684

order6552
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 580608
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3

Aliases

abelianC23×C32×C7×C13
multiplicative(ℤ/10191)ˣ, (ℤ/11487)ˣ, (ℤ/11613)ˣ, (ℤ/13588)ˣ, (ℤ/15316)ˣ, (ℤ/15484)ˣ, (ℤ/19692)ˣ, (ℤ/20382)ˣ, (ℤ/22974)ˣ, (ℤ/23226)ˣ

Subgroups

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

384 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6552 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C32×C4×C7×C13, C24×C32×C7×C13, C23×C3×C7×C9×C13, …
maximal normal subgroup ofC22×C32×C4×C7×C13, C24×C32×C7×C13, C23×C3×C7×C9×C13, …
maximal quotient ofC22×C32×C4×C7×C13, C24×C32×C7×C13, C23×C3×C7×C9×C13, …
automorphism group ofC3×C43×C79
outer automorphism group ofC3×C43×C79

GAP

Past the SmallGroups library coverage — no SmallGroups id.