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×#33590 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C67 |
| prime radical | C2×#508×C67 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ #117×C67 ◁ #405×C67 ◁ G | |
694 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 4 generators on 103 points:
(2,4)(5,6,11,16)(7,12,19,30)(8,14,10,26)(9,22,25,36)(13,31,33,18)(15,21,34,24)(17,27,20,29)(23,28,35,32)(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)(6,12)(8,20)(9,18)(10,17)(11,19)(13,22)(14,29)(15,28)(16,30)(21,35)(23,24)(25,31)(26,27)(32,34)(33,36);(5,7)(6,13)(8,17)(9,23)(10,20)(11,19)(12,22)(14,28)(15,29)(16,33)(18,24)(21,31)(25,35)(26,32)(27,34)(30,36);(5,8,11,10)(6,14,16,26)(7,17,19,20)(9,21,25,24)(12,27,30,29)(13,28,33,32)(15,22,34,36)(18,23,31,35)3082 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 26578);