Finite Group Databasebeta

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C23×C3×C7×C37 #72185394

order6216
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 72576
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC23×C3×C7×C37

Subgroups

subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

128 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6216 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC24×C3×C7×C37, C22×C3×C4×C7×C37, C23×C7×C9×C37, …
maximal normal subgroup ofC24×C3×C7×C37, C22×C3×C4×C7×C37, C23×C7×C9×C37, …
maximal quotient ofC24×C3×C7×C37, C22×C3×C4×C7×C37, C23×C7×C9×C37, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.