Finite Group Databasebeta

← Prev (#72190200) Next (#72190202) →

C22×C3×C4×C5×C49 #72190201

order11760
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 64512
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C3×C4×C5×C49
multiplicative(ℤ/15169)ˣ, (ℤ/17185)ˣ, (ℤ/18321)ˣ, (ℤ/18865)ˣ, (ℤ/19149)ˣ, (ℤ/19503)ˣ, (ℤ/22065)ˣ, (ℤ/22095)ˣ, (ℤ/23536)ˣ, (ℤ/24428)ˣ, (ℤ/25532)ˣ, (ℤ/25725)ˣ, (ℤ/29420)ˣ, (ℤ/30338)ˣ, (ℤ/34300)ˣ, (ℤ/34370)ˣ, (ℤ/36642)ˣ, (ℤ/37730)ˣ, (ℤ/38298)ˣ, (ℤ/39006)ˣ, (ℤ/44130)ˣ, (ℤ/44190)ˣ, (ℤ/51450)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C7C23×C3×C5×C7
socle, prime radicalC23×C3×C5×C7C2×C7
LCSG ▷ C1
UCSC1 ◁ G

324 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11760 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C5×C8×C49, C2×C3×C42×C5×C49, C23×C3×C4×C5×C49
maximal normal subgroup ofC22×C3×C5×C8×C49, C2×C3×C42×C5×C49, C23×C3×C4×C5×C49
maximal quotient ofC22×C3×C5×C8×C49, C2×C3×C42×C5×C49, C23×C3×C4×C5×C49
automorphism group ofC5×C11×C343, C3×C25×C343
outer automorphism group ofC5×C11×C343, C3×C25×C343

GAP

Past the SmallGroups library coverage — no SmallGroups id.