Finite Group Databasebeta

← Prev (#72187476) Next (#72187478) →

C3×C5×C9×C64 #72187477

order8640
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 13824
homologyAbelianization (H1) = G · Schur multiplier (H2) = C3

Aliases

abelianC3×C5×C9×C64

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3×C32C2×C32×C5
socle, prime radicalC2×C32×C5C3×C32
LCSG ▷ C1
UCSC1 ◁ G

140 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8640 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×C9×C128, C2×C3×C5×C9×C64, C3×C5×C27×C64, …
maximal normal subgroup ofC3×C5×C9×C128, C2×C3×C5×C9×C64, C3×C5×C27×C64, …
maximal quotient ofC3×C5×C9×C128, C2×C3×C5×C9×C64, C3×C5×C27×C64, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.