Finite Group Databasebeta

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C22×C3×C4×C11×C19 #72188701

order10032
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 69120
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C3×C4×C11×C19
multiplicative(ℤ/14665)ˣ, (ℤ/15801)ˣ, (ℤ/16341)ˣ, (ℤ/18855)ˣ, (ℤ/21068)ˣ, (ℤ/21788)ˣ, (ℤ/29330)ˣ, (ℤ/31602)ˣ, (ℤ/32682)ˣ, (ℤ/37710)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C3×C11×C19
socle, prime radicalC23×C3×C11×C19C2
LCSG ▷ C1
UCSC1 ◁ G

216 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10032 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C8×C11×C19, C2×C3×C42×C11×C19, C23×C3×C4×C11×C19, …
maximal normal subgroup ofC22×C3×C8×C11×C19, C2×C3×C42×C11×C19, C23×C3×C4×C11×C19, …
maximal quotient ofC22×C3×C8×C11×C19, C2×C3×C42×C11×C19, C23×C3×C4×C11×C19, …
automorphism group ofC5×C7×C419
outer automorphism group ofC5×C7×C419

GAP

Past the SmallGroups library coverage — no SmallGroups id.