Finite Group Databasebeta

← Prev (#72186607) Next (#72186609) →

C23×C3×C5×C82 #72186608

order7680
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 8455716864
homologyAbelianization (H1) = G · Schur multiplier (H2) = C29×C8

Aliases

abelianC23×C3×C5×C82
multiplicative(ℤ/27552)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC42C25×C3×C5
socle, prime radicalC25×C3×C5C42
LCSG ▷ C1
UCSC1 ◁ G

16648 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7680 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C3×C5×C8×C16, C22×C3×C4×C5×C82, C24×C3×C5×C82, …
maximal normal subgroup ofC23×C3×C5×C8×C16, C22×C3×C4×C5×C82, C24×C3×C5×C82, …
maximal quotient ofC23×C3×C5×C8×C16, C22×C3×C4×C5×C82, C24×C3×C5×C82, …
automorphism group ofC3×C7×C32×C41
outer automorphism group ofC3×C7×C32×C41

GAP

Past the SmallGroups library coverage — no SmallGroups id.