Finite Group Databasebeta

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C23×C7×C13×C16 #72190073

order11648
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 6193152
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC23×C7×C13×C16

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8C24×C7×C13
socle, prime radicalC24×C7×C13C8
LCSG ▷ C1
UCSC1 ◁ G

880 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 ofC23×C7×C13×C32, C24×C7×C13×C16, C22×C4×C7×C13×C16
maximal normal subgroup ofC23×C7×C13×C32, C24×C7×C13×C16, C22×C4×C7×C13×C16
maximal quotient ofC23×C7×C13×C32, C24×C7×C13×C16, C22×C4×C7×C13×C16

GAP

Past the SmallGroups library coverage — no SmallGroups id.