Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C67 · Schur multiplier (H2) = C210 |
| direct product | C2×C67×#2898 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C67 | C22×D4 |
| commutator | C4 | C24×C4×C67 |
| Frattini, cosocle | C2×C4 | C25×C67 |
| prime radical | C22×2−1+4×C67 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C67 ◁ C22×#41×C67 ◁ G | |
4882 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 5 generators on 89 points:
(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89);(3,4,5,6)(8,12)(10,17)(13,19)(14,18)(16,21)(20,22);(7,8,11,14)(9,13,15,20)(10,18,17,12)(16,22,21,19);(7,9)(8,13)(10,16)(11,15)(12,19)(14,20)(17,21)(18,22);(9,15)(13,20)(16,21)(19,22)5896 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 53073);