Finite Group Databasebeta

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C24×C32×C82 #72188010

order9216
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 97409858273280
homologyAbelianization (H1) = G · Schur multiplier (H2) = C214×C3×C8

Aliases

abelianC24×C32×C82

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC42C26×C32
socle, prime radicalC26×C32C42
LCSG ▷ C1
UCSC1 ◁ G

204414 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9216 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC24×C32×C8×C16, C23×C32×C4×C82, C25×C32×C82, …
maximal normal subgroup ofC24×C32×C8×C16, C23×C32×C4×C82, C25×C32×C82, …
maximal quotient ofC24×C32×C8×C16, C23×C32×C4×C82, C25×C32×C82, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.