Finite Group Databasebeta

← Prev (#72207994) Next (#72207996) →

C23×C3×C4×C52×C13 #72207995

order31200
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 247726080
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26×C5

Aliases

abelianC23×C3×C4×C52×C13
multiplicative(ℤ/50435)ˣ, (ℤ/54219)ˣ, (ℤ/56199)ˣ, (ℤ/60915)ˣ, (ℤ/63928)ˣ, (ℤ/64845)ˣ, (ℤ/64976)ˣ, (ℤ/65175)ˣ, (ℤ/68775)ˣ, (ℤ/72292)ˣ, (ℤ/74932)ˣ, (ℤ/81220)ˣ, (ℤ/86900)ˣ, (ℤ/91700)ˣ, (ℤ/95892)ˣ, (ℤ/100870)ˣ, (ℤ/108438)ˣ, (ℤ/112398)ˣ, (ℤ/117900)ˣ, (ℤ/121830)ˣ, (ℤ/129690)ˣ, (ℤ/130350)ˣ, (ℤ/137550)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C24×C3×C52×C13
socle, prime radicalC24×C3×C52×C13C2
LCSG ▷ C1
UCSC1 ◁ G

3776 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

31200 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.