Finite Group Databasebeta

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C24×C23×C29 #72189232

order10672
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 12418560
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC24×C23×C29
multiplicative(ℤ/22184)ˣ, (ℤ/33276)ˣ

Subgroups

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

268 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10672 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C4×C23×C29, C25×C23×C29, C24×C3×C23×C29
maximal normal subgroup ofC23×C4×C23×C29, C25×C23×C29, C24×C3×C23×C29
maximal quotient ofC23×C4×C23×C29, C25×C23×C29, C24×C3×C23×C29
automorphism group ofC8×C47×C59
outer automorphism group ofC8×C47×C59

GAP

Past the SmallGroups library coverage — no SmallGroups id.