Finite Group Databasebeta

← Prev (#72185406) Next (#72185408) →

C2×C3×C42×C5×C13 #72185407

order6240
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 147456
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C4

Aliases

abelianC2×C3×C42×C5×C13
multiplicative(ℤ/7579)ˣ, (ℤ/8215)ˣ, (ℤ/8515)ˣ, (ℤ/8635)ˣ, (ℤ/9275)ˣ, (ℤ/9295)ˣ, (ℤ/9699)ˣ, (ℤ/11775)ˣ, (ℤ/11925)ˣ, (ℤ/12675)ˣ, (ℤ/12932)ˣ, (ℤ/15158)ˣ, (ℤ/15700)ˣ, (ℤ/16430)ˣ, (ℤ/16900)ˣ, (ℤ/17030)ˣ, (ℤ/17270)ˣ, (ℤ/18550)ˣ, (ℤ/18590)ˣ, (ℤ/19398)ˣ, (ℤ/23550)ˣ, (ℤ/23850)ˣ, (ℤ/25350)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C23×C3×C5×C13
socle, prime radicalC23×C3×C5×C13C22
LCSG ▷ C1
UCSC1 ◁ G

432 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6240 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C4×C5×C8×C13, C3×C43×C5×C13, C22×C3×C42×C5×C13, …
maximal normal subgroup ofC2×C3×C4×C5×C8×C13, C3×C43×C5×C13, C22×C3×C42×C5×C13, …
maximal quotient ofC2×C3×C4×C5×C8×C13, C3×C43×C5×C13, C22×C3×C42×C5×C13, …
automorphism group ofC11×C13×C53, C5×C31×C53, C5×C13×C131, …
outer automorphism group ofC11×C13×C53, C5×C31×C53, C5×C13×C131, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.