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C2×C32×C42×C7×C13 #72203353

order26208
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5308416
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C3×C4

Aliases

abelianC2×C32×C42×C7×C13
multiplicative(ℤ/29627)ˣ, (ℤ/29783)ˣ, (ℤ/31871)ˣ, (ℤ/33755)ˣ, (ℤ/33761)ˣ, (ℤ/34307)ˣ, (ℤ/35555)ˣ, (ℤ/36335)ˣ, (ℤ/38255)ˣ, (ℤ/38465)ˣ, (ℤ/40977)ˣ, (ℤ/41405)ˣ, (ℤ/42627)ˣ, (ℤ/44109)ˣ, (ℤ/49185)ˣ, (ℤ/56836)ˣ, (ℤ/59254)ˣ, (ℤ/59566)ˣ, (ℤ/63742)ˣ, (ℤ/67510)ˣ, (ℤ/67522)ˣ, (ℤ/68614)ˣ, (ℤ/71110)ˣ, (ℤ/72670)ˣ, (ℤ/76510)ˣ, (ℤ/76930)ˣ, (ℤ/81954)ˣ, (ℤ/82810)ˣ, (ℤ/85254)ˣ, (ℤ/88218)ˣ, (ℤ/98370)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C23×C32×C7×C13
socle, prime radicalC23×C32×C7×C13C22
LCSG ▷ C1
UCSC1 ◁ G

1296 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

26208 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.