Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4×C32⋊H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C33 · Schur multiplier (H2) = C9 |
| direct product | Q8×#6898 |
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C2×C32 | C22×C33 |
| prime radical | C2×C33 | C22×C32 |
| LCS | G ▷ C2×C32 ▷ C1 | |
| UCS | C1 ◁ C2×C32 ◁ G | |
300 conjugacy classes of subgroups.
| minimal degree | μ(G) = 62 |
| transitive degree | μt(G) = 648 |
A minimal faithful permutation representation — 3 generators on 62 points:
(1,2,3,4)(5,8,7,6)(9,10,13)(11,15,21)(12,16,20)(14,22,19)(17,24,29)(18,25,28)(23,30,27)(26,32,34)(31,35,33)(36,37,40)(38,41,47)(39,43,48)(42,52,46)(44,49,55)(45,51,56)(50,59,54)(53,58,61)(57,62,60);(1,5,3,7)(2,6,4,8)(10,14,16)(13,20,22)(15,23,25)(21,28,30)(24,31,32)(29,34,35)(36,38,44,39,45,53,46,54,60)(37,41,49,43,51,58,42,50,57)(40,47,55,48,56,61,52,59,62);(9,11,17,19,27,33,12,18,26)(10,15,24,14,23,31,16,25,32)(13,21,29,22,30,35,20,28,34)(37,42,43)(40,48,52)(41,50,51)(47,56,59)(49,57,58)(55,61,62)255 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2237);