Finite Group DatabasebetaFinite Group Databasebeta| order | 1952 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C25 |
| direct product | H(5,𝔽2)×C61 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C61 | C24 |
| commutator, Frattini, cosocle | C2 | C24×C61 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C61 ◁ G | |
166 conjugacy classes of subgroups.
| minimal degree | μ(G) = 69 |
| transitive degree | μt(G) = 488 |
A minimal faithful permutation representation — 4 generators on 69 points:
(1,2)(3,7)(4,5)(6,8)(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69);(2,5)(6,7);(1,2)(3,6)(4,5)(7,8);(1,3)(2,6)(4,8)(5,7)1037 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1952, 49);