Finite Group Databasebeta

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C23×C7×C11×C17 #72189093

order10472
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 161280
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC23×C7×C11×C17
multiplicative(ℤ/16491)ˣ, (ℤ/21988)ˣ, (ℤ/32982)ˣ

Subgroups

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

128 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10472 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C4×C7×C11×C17, C24×C7×C11×C17, C23×C3×C7×C11×C17
maximal normal subgroup ofC22×C4×C7×C11×C17, C24×C7×C11×C17, C23×C3×C7×C11×C17
maximal quotient ofC22×C4×C7×C11×C17, C24×C7×C11×C17, C23×C3×C7×C11×C17

GAP

Past the SmallGroups library coverage — no SmallGroups id.