Finite Group Databasebeta

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C23×C32×C5×C29 #72189083

order10440
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 903168
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3

Aliases

abelianC23×C32×C5×C29
multiplicative(ℤ/12803)ˣ, (ℤ/16461)ˣ, (ℤ/25606)ˣ, (ℤ/32922)ˣ

Subgroups

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

384 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10440 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C32×C4×C5×C29, C24×C32×C5×C29, C23×C3×C5×C9×C29, …
maximal normal subgroup ofC22×C32×C4×C5×C29, C24×C32×C5×C29, C23×C3×C5×C9×C29, …
maximal quotient ofC22×C32×C4×C5×C29, C24×C32×C5×C29, C23×C3×C5×C9×C29, …
automorphism group ofC7×C31×C59
outer automorphism group ofC7×C31×C59

GAP

Past the SmallGroups library coverage — no SmallGroups id.