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C22×C4×C5×C7×C9 #72184402

order5040
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 27648
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C4×C5×C7×C9
multiplicative(ℤ/6061)ˣ, (ℤ/6745)ˣ, (ℤ/6985)ˣ, (ℤ/7881)ˣ, (ℤ/8613)ˣ, (ℤ/9465)ˣ, (ℤ/9525)ˣ, (ℤ/9585)ˣ, (ℤ/10096)ˣ, (ℤ/10508)ˣ, (ℤ/12122)ˣ, (ℤ/12620)ˣ, (ℤ/12700)ˣ, (ℤ/13490)ˣ, (ℤ/13970)ˣ, (ℤ/15762)ˣ, (ℤ/17226)ˣ, (ℤ/18930)ˣ, (ℤ/19050)ˣ, (ℤ/19170)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3C23×C3×C5×C7
socle, prime radicalC23×C3×C5×C7C2×C3
LCSG ▷ C1
UCSC1 ◁ G

324 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5040 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C5×C7×C8×C9, C2×C42×C5×C7×C9, C23×C4×C5×C7×C9, …
maximal normal subgroup ofC22×C5×C7×C8×C9, C2×C42×C5×C7×C9, C23×C4×C5×C7×C9, …
maximal quotient ofC22×C5×C7×C8×C9, C2×C42×C5×C7×C9, C23×C4×C5×C7×C9, …
automorphism group ofC11×C19×C29, C5×C19×C71, C5×C11×C127, …
outer automorphism group ofC11×C19×C29, C5×C19×C71, C5×C11×C127, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.