Finite Group Databasebeta

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C23×C23×C31 #72184960

order5704
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 110880
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC23×C23×C31
multiplicative(ℤ/11416)ˣ, (ℤ/17124)ˣ

Subgroups

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

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5704 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C4×C23×C31, C24×C23×C31, C23×C3×C23×C31, …
maximal normal subgroup ofC22×C4×C23×C31, C24×C23×C31, C23×C3×C23×C31, …
maximal quotient ofC22×C4×C23×C31, C24×C23×C31, C23×C3×C23×C31, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.