Finite Group Databasebeta

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C23×C3×C17×C23 #72188148

order9384
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 118272
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC23×C3×C17×C23
multiplicative(ℤ/14523)ˣ, (ℤ/18776)ˣ, (ℤ/19364)ˣ, (ℤ/28164)ˣ, (ℤ/29046)ˣ

Subgroups

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

128 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9384 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C4×C17×C23, C24×C3×C17×C23, C23×C9×C17×C23, …
maximal normal subgroup ofC22×C3×C4×C17×C23, C24×C3×C17×C23, C23×C9×C17×C23, …
maximal quotient ofC22×C3×C4×C17×C23, C24×C3×C17×C23, C23×C9×C17×C23, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.