Finite Group Databasebeta

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C23×C11×C41 #72183277

order3608
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 67200
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC23×C11×C41
multiplicative(ℤ/5727)ˣ, (ℤ/7636)ˣ, (ℤ/11454)ˣ

Subgroups

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

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3608 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C4×C11×C41, C24×C11×C41, C23×C3×C11×C41, …
maximal normal subgroup ofC22×C4×C11×C41, C24×C11×C41, C23×C3×C11×C41, …
maximal quotient ofC22×C4×C11×C41, C24×C11×C41, C23×C3×C11×C41, …
automorphism group ofC3×C23×C83, C4×C23×C83
outer automorphism group ofC3×C23×C83, C4×C23×C83

GAP

Past the SmallGroups library coverage — no SmallGroups id.