Finite Group Databasebeta

← Prev (#72188406) Next (#72188408) →

C32×C5×C8×C27 #72188407

order9720
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1119744
homologyAbelianization (H1) = G · Schur multiplier (H2) = C33

Aliases

abelianC32×C5×C8×C27

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4×C9C2×C33×C5
socle, prime radicalC2×C33×C5C4×C9
LCSG ▷ C1
UCSC1 ◁ G

576 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9720 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×C5×C16×C27, C2×C32×C5×C8×C27, C32×C5×C8×C81, …
maximal normal subgroup ofC32×C5×C16×C27, C2×C32×C5×C8×C27, C32×C5×C8×C81, …
maximal quotient ofC32×C5×C16×C27, C2×C32×C5×C8×C27, C32×C5×C8×C81, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.