Finite Group Databasebeta

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C22×C11×C16×C17 #72190372

order11968
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 122880
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C11×C16×C17
multiplicative(ℤ/19941)ˣ, (ℤ/26588)ˣ, (ℤ/39882)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8C23×C11×C17
socle, prime radicalC23×C11×C17C8
LCSG ▷ C1
UCSC1 ◁ G

196 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11968 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C11×C17×C32, C2×C4×C11×C16×C17, C23×C11×C16×C17
maximal normal subgroup ofC22×C11×C17×C32, C2×C4×C11×C16×C17, C23×C11×C16×C17
maximal quotient ofC22×C11×C17×C32, C2×C4×C11×C16×C17, C23×C11×C16×C17

GAP

Past the SmallGroups library coverage — no SmallGroups id.