Finite Group Databasebeta

← Prev (#72189284) Next (#72189286) →

C2×C43×C125 #72189285

order10750
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C2×C3×C4×C7×C25 (order 4200) · Inn(G) = C1 · Out(G) = C2×C3×C4×C7×C25
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC10750
abelianC2×C43×C125

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC25C2×C5×C43
socle, prime radicalC2×C5×C43C25
LCSG ▷ C1
UCSC1 ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10750 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofDic10750, D21500
maximal subgroup ofC4×C43×C125, C22×C43×C125, C2×C3×C43×C125, …
maximal normal subgroup ofC4×C43×C125, C22×C43×C125, C2×C3×C43×C125, …
maximal quotient ofC4×C43×C125, C22×C43×C125, C2×C3×C43×C125

GAP

Past the SmallGroups library coverage — no SmallGroups id.