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) = C2×C3 |
| direct product | D4×#6897 |
| unambiguous semidirect product | C4⋊(C2×#6897) |
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C2×C32 | C22×C33 |
| prime radical | C33×D4 | C32 |
| LCS | G ▷ C2×C32 ▷ C1 | |
| UCS | C1 ◁ C2×C32 ◁ G | |
400 conjugacy classes of subgroups.
| minimal degree | μ(G) = 58 |
| transitive degree | μt(G) = 324 |
A minimal faithful permutation representation — 3 generators on 58 points:
(1,2,3,4)(5,6,10)(7,14,27)(8,12,20)(9,13,21)(11,22,18)(15,24,30)(16,23,31)(17,25,28)(19,26,29)(32,33,36)(34,37,43)(35,39,44)(38,48,42)(40,45,51)(41,47,52)(46,55,50)(49,54,57)(53,58,56);(2,4)(5,7,15,9,8,16,19,18,17)(6,11,23,13,14,25,26,12,24)(10,20,28,21,22,30,29,27,31)(32,34,40,35,41,49,42,50,56)(33,37,45,39,47,54,38,46,53)(36,43,51,44,52,57,48,55,58);(5,8,17,9,18,15,19,7,16)(6,12,25,13,11,24,26,14,23)(10,20,28,21,22,30,29,27,31)(33,38,39)(36,44,48)(37,46,47)(43,52,55)(45,53,54)(51,57,58)255 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2206);