Finite Group Databasebeta

← Prev (#72188596) Next (#72188598) →

C22×C5×C16×C31 #72188597

order9920
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 92160
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C5×C16×C31
multiplicative(ℤ/15861)ˣ, (ℤ/19904)ˣ, (ℤ/21148)ˣ, (ℤ/31722)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8C23×C5×C31
socle, prime radicalC23×C5×C31C8
LCSG ▷ C1
UCSC1 ◁ G

196 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9920 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C5×C31×C32, C2×C4×C5×C16×C31, C23×C5×C16×C31, …
maximal normal subgroup ofC22×C5×C31×C32, C2×C4×C5×C16×C31, C23×C5×C16×C31, …
maximal quotient ofC22×C5×C31×C32, C2×C4×C5×C16×C31, C23×C5×C16×C31, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.