Finite Group Databasebeta

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C23×C4×C11×C41 #72192605

order14432
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 8601600
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC23×C4×C11×C41
multiplicative(ℤ/28635)ˣ, (ℤ/30544)ˣ, (ℤ/38180)ˣ, (ℤ/57270)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C24×C11×C41
socle, prime radicalC24×C11×C41C2
LCSG ▷ C1
UCSC1 ◁ G

472 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14432 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C8×C11×C41, C22×C42×C11×C41, C24×C4×C11×C41
maximal normal subgroup ofC23×C8×C11×C41, C22×C42×C11×C41, C24×C4×C11×C41
maximal quotient ofC23×C8×C11×C41, C22×C42×C11×C41, C24×C4×C11×C41
automorphism group ofC16×C23×C83
outer automorphism group ofC16×C23×C83

GAP

Past the SmallGroups library coverage — no SmallGroups id.