Finite Group Databasebeta

← Prev (#72189680) Next (#72189682) →

C22×C7×C16×C25 #72189681

order11200
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 92160
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C7×C16×C25
multiplicative(ℤ/22408)ˣ, (ℤ/33612)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC5×C8C23×C5×C7
socle, prime radicalC23×C5×C7C5×C8
LCSG ▷ C1
UCSC1 ◁ G

294 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11200 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C7×C25×C32, C2×C4×C7×C16×C25, C23×C7×C16×C25
maximal normal subgroup ofC22×C7×C25×C32, C2×C4×C7×C16×C25, C23×C7×C16×C25
maximal quotient ofC22×C7×C25×C32, C2×C4×C7×C16×C25, C23×C7×C16×C25

GAP

Past the SmallGroups library coverage — no SmallGroups id.