Finite Group Databasebeta

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C22×C3×C17×C32 #72185658

order6528
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 49152
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C3×C17×C32
multiplicative(ℤ/13184)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC16C23×C3×C17
socle, prime radicalC23×C3×C17C16
LCSG ▷ C1
UCSC1 ◁ G

240 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6528 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C17×C64, C2×C3×C4×C17×C32, C23×C3×C17×C32, …
maximal normal subgroup ofC22×C3×C17×C64, C2×C3×C4×C17×C32, C23×C3×C17×C32, …
maximal quotient ofC22×C3×C17×C64, C2×C3×C4×C17×C32, C23×C3×C17×C32, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.