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C22×C3×C11×C81 #72189244

order10692
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 58320
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C3

Aliases

abelianC22×C3×C11×C81
multiplicative(ℤ/10921)ˣ, (ℤ/12481)ˣ, (ℤ/16047)ˣ, (ℤ/16281)ˣ, (ℤ/21842)ˣ, (ℤ/24962)ˣ, (ℤ/32094)ˣ, (ℤ/32562)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC27C22×C32×C11
socle, prime radicalC22×C32×C11C27
LCSG ▷ C1
UCSC1 ◁ G

180 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10692 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C4×C11×C81, C23×C3×C11×C81, C22×C3×C11×C243, …
maximal normal subgroup ofC2×C3×C4×C11×C81, C23×C3×C11×C81, C22×C3×C11×C243, …
maximal quotient ofC2×C3×C4×C11×C81, C23×C3×C11×C81, C22×C3×C11×C243, …
automorphism group ofC67×C163, C7×C1783, C2×C67×C243
outer automorphism group ofC67×C163, C7×C1783, C2×C67×C243

GAP

Past the SmallGroups library coverage — no SmallGroups id.