Finite Group DatabasebetaFinite Group Databasebeta| order | 1952 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C61 · Schur multiplier (H2) = C22 |
| direct product | #131×C61 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C61 | C22 |
| commutator | C2 | C22×C4×C61 |
| Frattini, cosocle | C4 | C23×C61 |
| socle | C2×C61 | C22×C4 |
| prime radical | #41×C61 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C61 ◁ G | |
62 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 976 |
A minimal faithful permutation representation — 3 generators on 77 points:
(1,2,4,7,5,8,11,14)(3,6,10,13,9,12,15,16)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77);(1,3)(2,6)(4,10)(5,9)(7,13)(8,12)(11,15)(14,16);(3,9)(6,12)(10,15)(13,16)1220 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1952, 38);