Finite Group Databasebeta

← Prev (#72187970) Next (#72187972) →

C24×C32×C64 #72187971

order9216
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 7927234560
homologyAbelianization (H1) = G · Schur multiplier (H2) = C210×C3

Aliases

abelianC24×C32×C64
multiplicative(ℤ/32424)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC32C25×C32
socle, prime radicalC25×C32C32
LCSG ▷ C1
UCSC1 ◁ G

11454 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9216 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC24×C32×C128, C23×C32×C4×C64, C25×C32×C64, …
maximal normal subgroup ofC24×C32×C128, C23×C32×C4×C64, C25×C32×C64, …
maximal quotient ofC24×C32×C128, C23×C32×C4×C64, C25×C32×C64, …
automorphism group ofC3×C7×C8×C193
outer automorphism group ofC3×C7×C8×C193

GAP

Past the SmallGroups library coverage — no SmallGroups id.