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C22×C3×C4×C5×C9 #72182152

order2160
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 82944
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3

Aliases

abelianC22×C3×C4×C5×C9
multiplicative(ℤ/2717)ˣ, (ℤ/2849)ˣ, (ℤ/2945)ˣ, (ℤ/3325)ˣ, (ℤ/3441)ˣ, (ℤ/3477)ˣ, (ℤ/3663)ˣ, (ℤ/3801)ˣ, (ℤ/3861)ˣ, (ℤ/4185)ˣ, (ℤ/4275)ˣ, (ℤ/4588)ˣ, (ℤ/4636)ˣ, (ℤ/4725)ˣ, (ℤ/5068)ˣ, (ℤ/5434)ˣ, (ℤ/5698)ˣ, (ℤ/5890)ˣ, (ℤ/6516)ˣ, (ℤ/6588)ˣ, (ℤ/6650)ˣ, (ℤ/6882)ˣ, (ℤ/6954)ˣ, (ℤ/7326)ˣ, (ℤ/7602)ˣ, (ℤ/7722)ˣ, (ℤ/8370)ˣ, (ℤ/8550)ˣ, (ℤ/9450)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3C23×C32×C5
socle, prime radicalC23×C32×C5C2×C3
LCSG ▷ C1
UCSC1 ◁ G

540 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2160 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C5×C8×C9, C2×C3×C42×C5×C9, C23×C3×C4×C5×C9, …
maximal normal subgroup ofC22×C3×C5×C8×C9, C2×C3×C42×C5×C9, C23×C3×C4×C5×C9, …
maximal quotient ofC22×C3×C5×C8×C9, C2×C3×C42×C5×C9, C23×C3×C4×C5×C9, …
automorphism group ofC11×C13×C19, C7×C11×C37, C5×C19×C31, …
outer automorphism group ofC11×C13×C19, C7×C11×C37, C5×C19×C31, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.