Finite Group Databasebeta

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C24×C7×C8×C11 #72188564

order9856
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1238630400
homologyAbelianization (H1) = G · Schur multiplier (H2) = C210

Aliases

abelianC24×C7×C8×C11

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C25×C7×C11
socle, prime radicalC25×C7×C11C4
LCSG ▷ C1
UCSC1 ◁ G

3952 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9856 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC24×C7×C11×C16, C23×C4×C7×C8×C11, C25×C7×C8×C11, …
maximal normal subgroup ofC24×C7×C11×C16, C23×C4×C7×C8×C11, C25×C7×C8×C11, …
maximal quotient ofC24×C7×C11×C16, C23×C4×C7×C8×C11, C25×C7×C8×C11, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.