Finite Group Databasebeta

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C23×C3×C11×C37 #72188482

order9768
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 120960
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC23×C3×C11×C37
multiplicative(ℤ/15387)ˣ, (ℤ/20516)ˣ, (ℤ/30774)ˣ

Subgroups

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

128 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9768 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC24×C3×C11×C37, C22×C3×C4×C11×C37, C23×C9×C11×C37, …
maximal normal subgroup ofC24×C3×C11×C37, C22×C3×C4×C11×C37, C23×C9×C11×C37, …
maximal quotient ofC24×C3×C11×C37, C22×C3×C4×C11×C37, C23×C9×C11×C37, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.