Finite Group Databasebeta

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C23×C5×C157 #72185459

order6280
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 104832
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC23×C5×C157
multiplicative(ℤ/12568)ˣ, (ℤ/18852)ˣ

Subgroups

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

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6280 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC24×C5×C157, C22×C4×C5×C157, C23×C3×C5×C157, …
maximal normal subgroup ofC24×C5×C157, C22×C4×C5×C157, C23×C3×C5×C157, …
maximal quotient ofC24×C5×C157, C22×C4×C5×C157, C23×C3×C5×C157, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.