Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33522 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C25 |
| direct product | C67×#33586 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C67 |
| prime radical | C2×#509×C67 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ #117×C67 ◁ #405×C67 ◁ G | |
716 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 4 generators on 103 points:
(2,4)(5,6,10,15)(7,11,16,24)(8,12,21,28)(9,22,20,14)(13,29,27,19)(17,23,30,34)(18,33,31,26)(25,36,35,32)(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);(1,2,3,4)(5,7)(6,11)(8,17)(9,18)(10,16)(12,23)(13,25)(14,26)(15,24)(19,32)(20,31)(21,30)(22,33)(27,35)(28,34)(29,36);(6,12)(8,19)(9,20)(11,23)(13,14)(15,28)(17,32)(18,31)(21,29)(22,27)(24,34)(25,26)(30,36)(33,35);(7,16)(11,24)(17,30)(18,31)(23,34)(25,35)(26,33)(32,36)3082 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 26574);