Finite Group Databasebeta

← Prev (#72187445) Next (#72187447) →

C24×C3×C179 #72187446

order8592
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 7176960
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC24×C3×C179
multiplicative(ℤ/20104)ˣ, (ℤ/25848)ˣ, (ℤ/30156)ˣ

Subgroups

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

268 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8592 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C3×C4×C179, C25×C3×C179, C24×C9×C179, …
maximal normal subgroup ofC23×C3×C4×C179, C25×C3×C179, C24×C9×C179, …
maximal quotient ofC23×C3×C4×C179, C25×C3×C179, C24×C9×C179, …
automorphism group ofC7×C8×C359, C8×C9×C359
outer automorphism group ofC7×C8×C359, C8×C9×C359

GAP

Past the SmallGroups library coverage — no SmallGroups id.