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C22×C3×C7×C9×C16 #72190476

order12096
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 497664
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3

Aliases

abelianC22×C3×C7×C9×C16
multiplicative(ℤ/13889)ˣ, (ℤ/15029)ˣ, (ℤ/15113)ˣ, (ℤ/15827)ˣ, (ℤ/19209)ˣ, (ℤ/19323)ˣ, (ℤ/19431)ˣ, (ℤ/19737)ˣ, (ℤ/21189)ˣ, (ℤ/21357)ˣ, (ℤ/22491)ˣ, (ℤ/25612)ˣ, (ℤ/27778)ˣ, (ℤ/28252)ˣ, (ℤ/30058)ˣ, (ℤ/30226)ˣ, (ℤ/31654)ˣ, (ℤ/36324)ˣ, (ℤ/36396)ˣ, (ℤ/38418)ˣ, (ℤ/38646)ˣ, (ℤ/38862)ˣ, (ℤ/39474)ˣ, (ℤ/42378)ˣ, (ℤ/42714)ˣ, (ℤ/44982)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3×C8C23×C32×C7
socle, prime radicalC23×C32×C7C3×C8
LCSG ▷ C1
UCSC1 ◁ G

980 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12096 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C7×C9×C32, C2×C3×C4×C7×C9×C16, C23×C3×C7×C9×C16
maximal normal subgroup ofC22×C3×C7×C9×C32, C2×C3×C4×C7×C9×C16, C23×C3×C7×C9×C16
maximal quotient ofC22×C3×C7×C9×C32, C2×C3×C4×C7×C9×C16, C23×C3×C7×C9×C16
automorphism group ofC17×C19×C43, C17×C27×C43, C7×C27×C113, …
outer automorphism group ofC17×C19×C43, C17×C27×C43, C7×C27×C113, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.