Finite Group Databasebeta

← Prev (#72188737) Next (#72188739) →

C25×C32×C5×C7 #72188738

order10080
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 11519262720
homologyAbelianization (H1) = G · Schur multiplier (H2) = C210×C3

Aliases

abelianC25×C32×C5×C7
multiplicative(ℤ/26488)ˣ, (ℤ/31992)ˣ, (ℤ/34056)ˣ, (ℤ/35448)ˣ, (ℤ/35784)ˣ, (ℤ/36456)ˣ, (ℤ/38808)ˣ, (ℤ/39732)ˣ

Subgroups

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

8976 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10080 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC24×C32×C4×C5×C7, C26×C32×C5×C7, C25×C3×C5×C7×C9, …
maximal normal subgroup ofC24×C32×C4×C5×C7, C26×C32×C5×C7, C25×C3×C5×C7×C9, …
maximal quotient ofC24×C32×C4×C5×C7, C26×C32×C5×C7, C25×C3×C5×C7×C9, …
automorphism group ofC3×C4×C7×C11×C43, C7×C8×C11×C43, C3×C8×C31×C43
outer automorphism group ofC3×C4×C7×C11×C43, C7×C8×C11×C43, C3×C8×C31×C43

GAP

Past the SmallGroups library coverage — no SmallGroups id.