Finite Group Databasebeta

← Prev (#72189294) Next (#72189296) →

C3×C7×C16×C32 #72189295

order10752
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 393216
homologyAbelianization (H1) = G · Schur multiplier (H2) = C16

Aliases

abelianC3×C7×C16×C32
multiplicative(ℤ/10961)ˣ, (ℤ/11441)ˣ, (ℤ/21922)ˣ, (ℤ/22882)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8×C16C22×C3×C7
socle, prime radicalC22×C3×C7C8×C16
LCSG ▷ C1
UCSC1 ◁ G

456 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10752 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C7×C16×C64, C3×C7×C322, C2×C3×C7×C16×C32, …
maximal normal subgroup ofC3×C7×C16×C64, C3×C7×C322, C2×C3×C7×C16×C32, …
maximal quotient ofC3×C7×C16×C64, C3×C7×C322, C2×C3×C7×C16×C32, …
automorphism group ofC97×C113, C17×C673
outer automorphism group ofC97×C113, C17×C673

GAP

Past the SmallGroups library coverage — no SmallGroups id.