Finite Group Databasebeta

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C32×C11×C64 #72185484

order6336
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 15360
homologyAbelianization (H1) = G · Schur multiplier (H2) = C3

Aliases

abelianC32×C11×C64

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC32C2×C32×C11
socle, prime radicalC2×C32×C11C32
LCSG ▷ C1
UCSC1 ◁ G

84 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6336 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×C11×C128, C2×C32×C11×C64, C3×C9×C11×C64, …
maximal normal subgroup ofC32×C11×C128, C2×C32×C11×C64, C3×C9×C11×C64, …
maximal quotient ofC32×C11×C128, C2×C32×C11×C64, C3×C9×C11×C64, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.