Finite Group Databasebeta

← Prev (#72192024) Next (#72192026) →

C22×C3×C8×C9×C16 #72192025

order13824
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 339738624
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C3×C8

Aliases

abelianC22×C3×C8×C9×C16
multiplicative(ℤ/26061)ˣ, (ℤ/32704)ˣ, (ℤ/34748)ˣ, (ℤ/42048)ˣ, (ℤ/44676)ˣ, (ℤ/52122)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3×C4×C8C24×C32
socle, prime radicalC24×C32C3×C4×C8
LCSG ▷ C1
UCSC1 ◁ G

9620 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13824 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C8×C9×C32, C22×C3×C9×C162, C2×C3×C4×C8×C9×C16, …
maximal normal subgroup ofC22×C3×C8×C9×C32, C22×C3×C9×C162, C2×C3×C4×C8×C9×C16, …
maximal quotient ofC22×C3×C8×C9×C32, C22×C3×C9×C162, C2×C3×C4×C8×C9×C16, …
automorphism group ofC7×C64×C73
outer automorphism group ofC7×C64×C73

GAP

Past the SmallGroups library coverage — no SmallGroups id.