Finite Group Databasebeta

← Prev (#72188497) Next (#72188499) →

C22×C32×C16×C17 #72188498

order9792
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 589824
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3

Aliases

abelianC22×C32×C16×C17
multiplicative(ℤ/12257)ˣ, (ℤ/15759)ˣ, (ℤ/18207)ˣ, (ℤ/24514)ˣ, (ℤ/31518)ˣ, (ℤ/36414)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8C23×C32×C17
socle, prime radicalC23×C32×C17C8
LCSG ▷ C1
UCSC1 ◁ G

588 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9792 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C32×C17×C32, C2×C32×C4×C16×C17, C23×C32×C16×C17, …
maximal normal subgroup ofC22×C32×C17×C32, C2×C32×C4×C16×C17, C23×C32×C16×C17, …
maximal quotient ofC22×C32×C17×C32, C2×C32×C4×C16×C17, C23×C32×C16×C17, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.