Finite Group Databasebeta

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C23×C3×C8×C41 #72186789

order7872
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 3440640
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC23×C3×C8×C41
multiplicative(ℤ/18592)ˣ, (ℤ/23904)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C24×C3×C41
socle, prime radicalC24×C3×C41C4
LCSG ▷ C1
UCSC1 ◁ G

676 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7872 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C3×C16×C41, C22×C3×C4×C8×C41, C24×C3×C8×C41, …
maximal normal subgroup ofC23×C3×C16×C41, C22×C3×C4×C8×C41, C24×C3×C8×C41, …
maximal quotient ofC23×C3×C16×C41, C22×C3×C4×C8×C41, C24×C3×C8×C41, …
automorphism group ofC7×C32×C83, C9×C32×C83
outer automorphism group ofC7×C32×C83, C9×C32×C83

GAP

Past the SmallGroups library coverage — no SmallGroups id.