Finite Group Databasebeta

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C23×C5×C9×C41 #72192858

order14760
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 161280
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC23×C5×C9×C41
multiplicative(ℤ/17347)ˣ, (ℤ/24387)ˣ, (ℤ/24651)ˣ, (ℤ/29528)ˣ, (ℤ/32516)ˣ, (ℤ/34694)ˣ, (ℤ/44292)ˣ, (ℤ/48774)ˣ, (ℤ/49302)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3C23×C3×C5×C41
socle, prime radicalC23×C3×C5×C41C3
LCSG ▷ C1
UCSC1 ◁ G

192 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14760 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C4×C5×C9×C41, C24×C5×C9×C41
maximal normal subgroup ofC22×C4×C5×C9×C41, C24×C5×C9×C41
maximal quotient ofC22×C4×C5×C9×C41, C24×C5×C9×C41
automorphism group ofC11×C19×C83, C11×C27×C83
outer automorphism group ofC11×C19×C83, C11×C27×C83

GAP

Past the SmallGroups library coverage — no SmallGroups id.