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C2×C3×C4×C7×C9×C16 #72201469

order24192
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 2654208
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C3×C4

Aliases

abelianC2×C3×C4×C7×C9×C16
multiplicative(ℤ/27047)ˣ, (ℤ/27911)ˣ, (ℤ/28067)ˣ, (ℤ/29267)ˣ, (ℤ/30821)ˣ, (ℤ/32015)ˣ, (ℤ/35315)ˣ, (ℤ/37407)ˣ, (ℤ/37629)ˣ, (ℤ/39351)ˣ, (ℤ/39663)ˣ, (ℤ/45405)ˣ, (ℤ/45495)ˣ, (ℤ/49876)ˣ, (ℤ/52468)ˣ, (ℤ/54094)ˣ, (ℤ/55822)ˣ, (ℤ/56134)ˣ, (ℤ/58534)ˣ, (ℤ/61642)ˣ, (ℤ/64030)ˣ, (ℤ/70630)ˣ, (ℤ/74814)ˣ, (ℤ/75258)ˣ, (ℤ/78702)ˣ, (ℤ/79326)ˣ, (ℤ/90810)ˣ, (ℤ/90990)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3×C8C23×C32×C7
socle, prime radicalC23×C32×C7C2×C3×C8
LCSG ▷ C1
UCSC1 ◁ G

2160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

24192 conjugacy classes. The character table is too large to display.

Relationships

automorphism group ofC17×C37×C43
outer automorphism group ofC17×C37×C43

GAP

Past the SmallGroups library coverage — no SmallGroups id.