Finite Group Databasebeta

← Prev (#72193150) Next (#72193152) →

C3×C42×C5×C7×C9 #72193151

order15120
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 248832
homologyAbelianization (H1) = G · Schur multiplier (H2) = C3×C4

Aliases

abelianC3×C42×C5×C7×C9
multiplicative(ℤ/15577)ˣ, (ℤ/31154)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22×C3C22×C32×C5×C7
socle, prime radicalC22×C32×C5×C7C22×C3
LCSG ▷ C1
UCSC1 ◁ G

600 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15120 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C4×C5×C7×C8×C9, C2×C3×C42×C5×C7×C9
maximal normal subgroup ofC3×C4×C5×C7×C8×C9, C2×C3×C42×C5×C7×C9
maximal quotient ofC3×C4×C5×C7×C8×C9, C2×C3×C42×C5×C7×C9
automorphism group ofC37×C421
outer automorphism group ofC37×C421

GAP

Past the SmallGroups library coverage — no SmallGroups id.