Finite Group Databasebeta

← Prev (#72189682) Next (#72189684) →

C22×C52×C7×C16 #72189683

order11200
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 2211840
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C5

Aliases

abelianC22×C52×C7×C16
multiplicative(ℤ/13277)ˣ, (ℤ/26554)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8C23×C52×C7
socle, prime radicalC23×C52×C7C8
LCSG ▷ C1
UCSC1 ◁ G

784 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×C52×C7×C32, C2×C4×C52×C7×C16, C23×C52×C7×C16
maximal normal subgroup ofC22×C52×C7×C32, C2×C4×C52×C7×C16, C23×C52×C7×C16
maximal quotient ofC22×C52×C7×C32, C2×C4×C52×C7×C16, C23×C52×C7×C16
automorphism group ofC11×C17×C71
outer automorphism group ofC11×C17×C71

GAP

Past the SmallGroups library coverage — no SmallGroups id.