Finite Group Databasebeta

← Prev (#72190678) Next (#72190680) →

C22×C3×C43×C16 #72190679

order12288
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 2216615441596416
homologyAbelianization (H1) = G · Schur multiplier (H2) = C29×C46

Aliases

abelianC22×C3×C43×C16
multiplicative(ℤ/53040)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC23×C8C26×C3
socle, prime radicalC26×C3C23×C8
LCSG ▷ C1
UCSC1 ◁ G

581238 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12288 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C43×C32, C22×C3×C42×C8×C16, C2×C3×C44×C16, …
maximal normal subgroup ofC22×C3×C43×C32, C22×C3×C42×C8×C16, C2×C3×C44×C16, …
maximal quotient ofC22×C3×C43×C32, C22×C3×C42×C8×C16, C2×C3×C44×C16, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.