Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C67 · Schur multiplier (H2) = C25×C4 |
| direct product | C67×#20422 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C67 | C22×D4 |
| commutator | C4 | C22×C42×C67 |
| Frattini, cosocle | C22×C4 | C24×C67 |
| socle | C22×C67 | C2×C4×D4 |
| prime radical | C22×#41×C67 | C22 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C67 ◁ C22×M16×C67 ◁ G | |
1458 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 4 generators on 103 points:
(1,2)(3,4)(5,6,10,14,11,15,9,24)(7,16,20,26,18,30,19,12)(8,13,23,28,21,27,22,34)(17,29,32,35,33,36,31,25)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103);(2,4)(5,7)(6,12,15,26)(8,17)(9,19)(10,20)(11,18)(13,25,27,35)(14,16,24,30)(21,33)(22,31)(23,32)(28,29,34,36);(5,8,10,23,11,21,9,22)(6,13,14,28,15,27,24,34)(7,17,20,32,18,33,19,31)(12,25,16,29,26,35,30,36);(7,18)(8,21)(12,26)(13,27)(16,30)(19,20)(22,23)(28,34)5896 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 13410);