Finite Group Databasebeta

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C23×C3×C64 #72181971

order1536
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 688128
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC23×C3×C64
multiplicative(ℤ/4632)ˣ, (ℤ/5376)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC32C24×C3
socle, prime radicalC24×C3C32
LCSG ▷ C1
UCSC1 ◁ G

644 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1536 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C3×C128, C24×C3×C64, C22×C3×C4×C64, …
maximal normal subgroup ofC23×C3×C128, C24×C3×C64, C22×C3×C4×C64, …
maximal quotient ofC23×C3×C128, C24×C3×C64, C22×C3×C4×C64, …
automorphism group ofC3×C8×C193, C3×C7×C256
outer automorphism group ofC3×C8×C193, C3×C7×C256

GAP

Past the SmallGroups library coverage — no SmallGroups id.