Finite Group Databasebeta

← Prev (#72183228) Next (#72183230) →

C23×C7×C64 #72183229

order3584
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 2064384
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC23×C7×C64
multiplicative(ℤ/10776)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC32C24×C7
socle, prime radicalC24×C7C32
LCSG ▷ C1
UCSC1 ◁ G

644 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3584 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C7×C128, C24×C7×C64, C22×C4×C7×C64, …
maximal normal subgroup ofC23×C7×C128, C24×C7×C64, C22×C4×C7×C64, …
maximal quotient ofC23×C7×C128, C24×C7×C64, C22×C4×C7×C64, …
automorphism group ofC3×C8×C449
outer automorphism group ofC3×C8×C449

GAP

Past the SmallGroups library coverage — no SmallGroups id.