Finite Group Databasebeta

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C22×C32×C11×C16 #72185490

order6336
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 368640
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3

Aliases

abelianC22×C32×C11×C16
multiplicative(ℤ/7973)ˣ, (ℤ/10251)ˣ, (ℤ/15946)ˣ, (ℤ/20502)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8C23×C32×C11
socle, prime radicalC23×C32×C11C8
LCSG ▷ C1
UCSC1 ◁ G

588 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6336 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C32×C11×C32, C2×C32×C4×C11×C16, C23×C32×C11×C16, …
maximal normal subgroup ofC22×C32×C11×C32, C2×C32×C4×C11×C16, C23×C32×C11×C16, …
maximal quotient ofC22×C32×C11×C32, C2×C32×C4×C11×C16, C23×C32×C11×C16, …
automorphism group ofC7×C17×C67, C9×C17×C67
outer automorphism group ofC7×C17×C67, C9×C17×C67

GAP

Past the SmallGroups library coverage — no SmallGroups id.