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C22×C4×C5×C9×C11 #72186832

order7920
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 46080
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C4×C5×C9×C11
multiplicative(ℤ/9361)ˣ, (ℤ/10925)ˣ, (ℤ/10945)ˣ, (ℤ/11495)ˣ, (ℤ/12489)ˣ, (ℤ/13101)ˣ, (ℤ/13431)ˣ, (ℤ/14865)ˣ, (ℤ/14925)ˣ, (ℤ/15525)ˣ, (ℤ/15856)ˣ, (ℤ/16335)ˣ, (ℤ/16652)ˣ, (ℤ/17468)ˣ, (ℤ/17908)ˣ, (ℤ/18722)ˣ, (ℤ/19820)ˣ, (ℤ/19900)ˣ, (ℤ/21850)ˣ, (ℤ/21890)ˣ, (ℤ/22990)ˣ, (ℤ/24978)ˣ, (ℤ/26202)ˣ, (ℤ/26862)ˣ, (ℤ/29730)ˣ, (ℤ/29850)ˣ, (ℤ/31050)ˣ, (ℤ/32670)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3C23×C3×C5×C11
socle, prime radicalC23×C3×C5×C11C2×C3
LCSG ▷ C1
UCSC1 ◁ G

324 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×C5×C8×C9×C11, C2×C42×C5×C9×C11, C23×C4×C5×C9×C11, …
maximal normal subgroup ofC22×C5×C8×C9×C11, C2×C42×C5×C9×C11, C23×C4×C5×C9×C11, …
maximal quotient ofC22×C5×C8×C9×C11, C2×C42×C5×C9×C11, C23×C4×C5×C9×C11, …
automorphism group ofC11×C23×C37, C19×C23×C25, C5×C11×C199, …
outer automorphism group ofC11×C23×C37, C19×C23×C25, C5×C11×C199, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.