Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C67 · Schur multiplier (H2) = C28 |
| direct product | C2×C67×#1791 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C67 | #120 |
| commutator | C23 | C23×C4×C67 |
| Frattini, cosocle | C22×C4 | C24×C67 |
| socle | C22×C67 | #379 |
| prime radical | C2×#585×C67 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C67 ◁ C23×C4×C67 ◁ G | |
3662 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 4 generators on 101 points:
(1,2)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101);(3,4,7,12,8,11,20,25)(5,13,16,26,15,9,19,22)(6,10,18,23,17,24,30,34)(14,21,29,32,28,27,31,33);(3,5)(4,9)(6,14)(7,19)(8,15)(10,21)(11,13)(12,26)(16,20)(17,28)(18,31)(22,25)(23,33)(24,27)(29,30)(32,34);(3,6)(4,10)(5,14)(7,18)(8,17)(9,21)(11,24)(12,23)(13,27)(15,28)(16,29)(19,31)(20,30)(22,32)(25,34)(26,33)4288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 13599);