Finite Group Databasebeta

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C23×C17×C37 #72184396

order5032
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 96768
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC23×C17×C37
multiplicative(ℤ/10072)ˣ, (ℤ/15108)ˣ

Subgroups

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

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5032 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C4×C17×C37, C24×C17×C37, C23×C3×C17×C37, …
maximal normal subgroup ofC22×C4×C17×C37, C24×C17×C37, C23×C3×C17×C37, …
maximal quotient ofC22×C4×C17×C37, C24×C17×C37, C23×C3×C17×C37, …
automorphism group ofC8×C1259
outer automorphism group ofC8×C1259

GAP

Past the SmallGroups library coverage — no SmallGroups id.