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C23×C23×C32 #19181597

order5888
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 3784704
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC23×C23×C32
multiplicative(ℤ/18048)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
FrattiniC16C24×C23
socleC24×C23C16
LCSG ▷ C1
UCSC1 ◁ G

542 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5888 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C23×C64, C24×C23×C32, C22×C4×C23×C32, …
maximal normal subgroup ofC23×C23×C64, C24×C23×C32, C22×C4×C23×C32, …
maximal quotient ofC23×C23×C64, C24×C23×C32, C22×C4×C23×C32, …
automorphism group ofC3×C47×C128
outer automorphism group ofC3×C47×C128

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5888, 26959);