Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of C32⋊H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33×C4 · Schur multiplier (H2) = C2×C9 |
| direct product | C2×C4×#6898 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C32×C4 | C33 |
| commutator | C32 | C2×C33×C4 |
| Frattini, cosocle | C2×C32 | C22×C33 |
| socle | C22×C32 | C2×C33 |
| prime radical | C22×C33 | C2×C32 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C2×C32×C4 ◁ G | |
400 conjugacy classes of subgroups.
| minimal degree | μ(G) = 60 |
| transitive degree | μt(G) = 648 |
A minimal faithful permutation representation — 3 generators on 60 points:
(1,2)(7,8,11)(9,13,19)(10,14,18)(12,20,17)(15,22,27)(16,23,26)(21,28,25)(24,30,32)(29,33,31)(34,35,38)(36,39,45)(37,41,46)(40,50,44)(42,47,53)(43,49,54)(48,57,52)(51,56,59)(55,60,58);(3,4,5,6)(8,12,14)(11,18,20)(13,21,23)(19,26,28)(22,29,30)(27,32,33)(34,36,42,37,43,51,44,52,58)(35,39,47,41,49,56,40,48,55)(38,45,53,46,54,59,50,57,60);(7,9,15,17,25,31,10,16,24)(8,13,22,12,21,29,14,23,30)(11,19,27,20,28,33,18,26,32)(35,40,41)(38,46,50)(39,48,49)(45,54,57)(47,55,56)(53,59,60)408 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2177);