Finite Group Databasebeta

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C32×C5×C9×C16 #72185608

order6480
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 746496
homologyAbelianization (H1) = G · Schur multiplier (H2) = C33

Aliases

abelianC32×C5×C9×C16

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3×C8C2×C33×C5
socle, prime radicalC2×C33×C5C3×C8
LCSG ▷ C1
UCSC1 ◁ G

500 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6480 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×C5×C9×C32, C2×C32×C5×C9×C16, C32×C5×C16×C27, …
maximal normal subgroup ofC32×C5×C9×C32, C2×C32×C5×C9×C16, C32×C5×C16×C27, …
maximal quotient ofC32×C5×C9×C32, C2×C32×C5×C9×C16, C32×C5×C16×C27, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.