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C2×C32×C42×C5×C13 #72196489

order18720
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 3538944
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C3×C4

Aliases

abelianC2×C32×C42×C5×C13
multiplicative(ℤ/21359)ˣ, (ℤ/22451)ˣ, (ℤ/22631)ˣ, (ℤ/24095)ˣ, (ℤ/24335)ˣ, (ℤ/25675)ˣ, (ℤ/26195)ˣ, (ℤ/27475)ˣ, (ℤ/28731)ˣ, (ℤ/29097)ˣ, (ℤ/29575)ˣ, (ℤ/30927)ˣ, (ℤ/35325)ˣ, (ℤ/38025)ˣ, (ℤ/38308)ˣ, (ℤ/41236)ˣ, (ℤ/42718)ˣ, (ℤ/44902)ˣ, (ℤ/45262)ˣ, (ℤ/48190)ˣ, (ℤ/48670)ˣ, (ℤ/51350)ˣ, (ℤ/52390)ˣ, (ℤ/54950)ˣ, (ℤ/57462)ˣ, (ℤ/58194)ˣ, (ℤ/59150)ˣ, (ℤ/61854)ˣ, (ℤ/70650)ˣ, (ℤ/76050)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C23×C32×C5×C13
socle, prime radicalC23×C32×C5×C13C22
LCSG ▷ C1
UCSC1 ◁ G

1296 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

18720 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.