Finite Group Databasebeta

← Prev (#44570495) Next (#44570497) →

C2×C32×C5×C192 #44570496

order32490
nilpotency class1
automorphism?
homologyAbelianization (H1) = G · Schur multiplier (H2) = C3×C19

Aliases

abelianC2×C32×C5×C192

Subgroups

subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

528 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 51
transitive degreeμt(G) = 32490

A minimal faithful permutation representation — 2 generators on 51 points:

(1,2)(3,4,5)(9,10,11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32);(6,7,8)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51)

Conjugacy classes & character table

32490 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32490, 80);