Finite Group Databasebeta

← Prev (#72186832) Next (#72186834) →

C22×C32×C4×C5×C11 #72186833

order7920
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 368640
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3

Aliases

abelianC22×C32×C4×C5×C11
multiplicative(ℤ/9269)ˣ, (ℤ/9581)ˣ, (ℤ/9821)ˣ, (ℤ/10385)ˣ, (ℤ/11011)ˣ, (ℤ/11585)ˣ, (ℤ/11725)ˣ, (ℤ/12261)ˣ, (ℤ/12627)ˣ, (ℤ/12909)ˣ, (ℤ/13881)ˣ, (ℤ/14157)ˣ, (ℤ/14895)ˣ, (ℤ/15075)ˣ, (ℤ/16348)ˣ, (ℤ/17212)ˣ, (ℤ/18508)ˣ, (ℤ/18538)ˣ, (ℤ/19162)ˣ, (ℤ/19642)ˣ, (ℤ/20770)ˣ, (ℤ/22022)ˣ, (ℤ/23170)ˣ, (ℤ/23450)ˣ, (ℤ/23796)ˣ, (ℤ/24522)ˣ, (ℤ/25254)ˣ, (ℤ/25818)ˣ, (ℤ/27762)ˣ, (ℤ/28314)ˣ, (ℤ/29790)ˣ, (ℤ/30150)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C32×C5×C11
socle, prime radicalC23×C32×C5×C11C2
LCSG ▷ C1
UCSC1 ◁ G

648 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7920 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C32×C5×C8×C11, C2×C32×C42×C5×C11, C23×C32×C4×C5×C11, …
maximal normal subgroup ofC22×C32×C5×C8×C11, C2×C32×C42×C5×C11, C23×C32×C4×C5×C11, …
maximal quotient ofC22×C32×C5×C8×C11, C2×C32×C42×C5×C11, C23×C32×C4×C5×C11, …
automorphism group ofC13×C23×C31, C11×C13×C67, C7×C23×C61, …
outer automorphism group ofC13×C23×C31, C11×C13×C67, C7×C23×C61, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.