Finite Group Databasebeta

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C24×C7×C8×C13 #72190076

order11648
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1486356480
homologyAbelianization (H1) = G · Schur multiplier (H2) = C210

Aliases

abelianC24×C7×C8×C13

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C25×C7×C13
socle, prime radicalC25×C7×C13C4
LCSG ▷ C1
UCSC1 ◁ G

3952 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11648 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC24×C7×C13×C16, C23×C4×C7×C8×C13, C25×C7×C8×C13
maximal normal subgroup ofC24×C7×C13×C16, C23×C4×C7×C8×C13, C25×C7×C8×C13
maximal quotient ofC24×C7×C13×C16, C23×C4×C7×C8×C13, C25×C7×C8×C13

GAP

Past the SmallGroups library coverage — no SmallGroups id.