Finite Group Databasebeta

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C23×C3×C5×C7×C13 #72189463

order10920
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 96768
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC23×C3×C5×C7×C13
multiplicative(ℤ/16827)ˣ, (ℤ/16899)ˣ, (ℤ/18051)ˣ, (ℤ/19131)ˣ, (ℤ/19257)ˣ, (ℤ/21848)ˣ, (ℤ/22436)ˣ, (ℤ/22532)ˣ, (ℤ/24068)ˣ, (ℤ/25508)ˣ, (ℤ/25676)ˣ, (ℤ/32772)ˣ, (ℤ/32796)ˣ, (ℤ/33654)ˣ, (ℤ/33798)ˣ, (ℤ/36102)ˣ, (ℤ/38262)ˣ, (ℤ/38514)ˣ

Subgroups

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

256 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10920 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C4×C5×C7×C13, C24×C3×C5×C7×C13, C23×C5×C7×C9×C13, …
maximal normal subgroup ofC22×C3×C4×C5×C7×C13, C24×C3×C5×C7×C13, C23×C5×C7×C9×C13, …
maximal quotient ofC22×C3×C4×C5×C7×C13, C24×C3×C5×C7×C13, C23×C5×C7×C9×C13, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.