Finite Group Databasebeta

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C23×C23×C29 #72184657

order5336
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 103488
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC23×C23×C29
multiplicative(ℤ/8319)ˣ, (ℤ/11092)ˣ, (ℤ/16638)ˣ

Subgroups

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

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5336 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C4×C23×C29, C24×C23×C29, C23×C3×C23×C29, …
maximal normal subgroup ofC22×C4×C23×C29, C24×C23×C29, C23×C3×C23×C29, …
maximal quotient ofC22×C4×C23×C29, C24×C23×C29, C23×C3×C23×C29, …
automorphism group ofC3×C47×C59, C4×C47×C59
outer automorphism group ofC3×C47×C59, C4×C47×C59

GAP

Past the SmallGroups library coverage — no SmallGroups id.