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C2×C3×C4×C8×C9×C13 #72199869

order22464
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 2654208
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C3×C4

Aliases

abelianC2×C3×C4×C8×C9×C13
multiplicative(ℤ/27083)ˣ, (ℤ/28835)ˣ, (ℤ/29735)ˣ, (ℤ/32795)ˣ, (ℤ/34383)ˣ, (ℤ/34743)ˣ, (ℤ/34821)ˣ, (ℤ/36543)ˣ, (ℤ/37011)ˣ, (ℤ/42165)ˣ, (ℤ/42255)ˣ, (ℤ/45844)ˣ, (ℤ/46324)ˣ, (ℤ/48724)ˣ, (ℤ/49348)ˣ, (ℤ/54166)ˣ, (ℤ/57670)ˣ, (ℤ/59470)ˣ, (ℤ/65590)ˣ, (ℤ/68766)ˣ, (ℤ/69486)ˣ, (ℤ/69642)ˣ, (ℤ/73086)ˣ, (ℤ/74022)ˣ, (ℤ/84330)ˣ, (ℤ/84510)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3×C4C23×C32×C13
socle, prime radicalC23×C32×C13C2×C3×C4
LCSG ▷ C1
UCSC1 ◁ G

1620 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

22464 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.