Finite Group Databasebeta

← Prev (#72184398) Next (#72184400) →

C42×C5×C7×C9 #72184399

order5040
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 13824
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4

Aliases

abelianC42×C5×C7×C9
multiplicative(ℤ/5249)ˣ, (ℤ/10498)ˣ

Subgroups

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

180 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5040 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C5×C7×C8×C9, C2×C42×C5×C7×C9, C42×C5×C7×C27, …
maximal normal subgroup ofC4×C5×C7×C8×C9, C2×C42×C5×C7×C9, C42×C5×C7×C27, …
maximal quotient ofC4×C5×C7×C8×C9, C2×C42×C5×C7×C9, C42×C5×C7×C27, …
automorphism group ofC29×C181, C2×C29×C181
outer automorphism group ofC29×C181, C2×C29×C181

GAP

Past the SmallGroups library coverage — no SmallGroups id.