Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C67 · Schur multiplier (H2) = C25 |
| direct product | C67×#33436 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C67 | C24 |
| commutator | C22 | C23×C8×C67 |
| Frattini, cosocle | C2×C8 | C24×C67 |
| socle | C22×C67 | C23×C8 |
| prime radical | #525×C67 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C67 ◁ G | |
692 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)(5,6,8,12,9,13,18,24,10,14,19,25,20,26,30,34)(7,11,16,22,17,23,29,33,15,21,27,31,28,32,35,36)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103);(2,4);(5,7,8,16,9,17,18,29,10,15,19,27,20,28,30,35)(6,11,12,22,13,23,24,33,14,21,25,31,26,32,34,36);(7,15)(11,21)(16,27)(17,28)(22,31)(23,32)(29,35)(33,36)6700 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 26424);