Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32×C9 · Schur multiplier (H2) = C23×C32 |
| direct product | C23×#6903 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C27 | C32 |
| commutator | C3 | C23×C32×C9 |
| Frattini, cosocle | C9 | C23×C33 |
| socle | C23×C3 | C32×C9 |
| prime radical | C23×H(3,𝔽3) | C9 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C23×C27 ◁ G | |
880 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 648 |
A minimal faithful permutation representation — 3 generators on 87 points:
(1,2)(7,8,12,10,14,24,20,30,45,11,15,25,21,31,46,39,54,68,22,32,47,40,55,69,61,75,83)(9,13,23,18,28,43,37,52,66,19,29,44,38,53,67,60,74,82,17,27,42,36,51,65,59,73,81)(16,26,41,34,49,63,57,71,79,33,48,62,56,70,78,76,84,86,35,50,64,58,72,80,77,85,87);(3,4)(7,9,16)(8,13,26)(10,18,34)(11,19,33)(12,23,41)(14,28,49)(15,29,48)(17,35,22)(20,37,57)(21,38,56)(24,43,63)(25,44,62)(27,50,32)(30,52,71)(31,53,70)(36,58,40)(39,60,76)(42,64,47)(45,66,79)(46,67,78)(51,72,55)(54,74,84)(59,77,61)(65,80,69)(68,82,86)(73,85,75)(81,87,83);(5,6)(9,17,19)(13,27,29)(16,33,35)(18,36,38)(23,42,44)(26,48,50)(28,51,53)(34,56,58)(37,59,60)(41,62,64)(43,65,67)(49,70,72)(52,73,74)(57,76,77)(63,78,80)(66,81,82)(71,84,85)(79,86,87)792 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2965);