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C23×C29×C32 #20328871

order7424
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 4816896
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC23×C29×C32
multiplicative(ℤ/22296)ˣ, (ℤ/22656)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
FrattiniC16C24×C29
socleC24×C29C16
LCSG ▷ C1
UCSC1 ◁ G

542 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7424 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C29×C64, C22×C4×C29×C32, C24×C29×C32, …
maximal normal subgroup ofC23×C29×C64, C22×C4×C29×C32, C24×C29×C32, …
maximal quotient ofC23×C29×C64, C22×C4×C29×C32, C24×C29×C32, …
automorphism group ofC3×C8×C929, C3×C59×C128
outer automorphism group ofC3×C8×C929, C3×C59×C128

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7424, 26959);