Finite Group Databasebeta

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C23×C33×C17 #72183307

order3672
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 30191616
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C33

Aliases

abelianC23×C33×C17
multiplicative(ℤ/6489)ˣ, (ℤ/12978)ˣ

Subgroups

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

896 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3672 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C33×C4×C17, C24×C33×C17, C23×C32×C9×C17, …
maximal normal subgroup ofC22×C33×C4×C17, C24×C33×C17, C23×C32×C9×C17, …
maximal quotient ofC22×C33×C4×C17, C24×C33×C17, C23×C32×C9×C17, …
automorphism group ofC7×C9×C103
outer automorphism group ofC7×C9×C103

GAP

Past the SmallGroups library coverage — no SmallGroups id.