Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C67 · Schur multiplier (H2) = C29 |
| direct product | C67×#60175 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C23×D4 |
| commutator | C4 | C24×C4×C67 |
| Frattini, cosocle | C2×C4 | C25×C67 |
| prime radical | C2×#578×C67 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C4×#41×C67 ◁ G | |
2650 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 5 generators on 103 points:
(1,2,4,3)(5,6)(7,15)(8,13)(9,21)(10,12)(11,17)(14,23)(16,29)(18,28)(19,26)(20,33)(22,24)(25,31)(27,32)(30,36)(34,35)(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);(5,7,10,18)(6,11,12,24)(8,16,19,30)(9,22,23,17)(13,25,26,35)(14,28,21,15)(20,34,32,31)(27,36,33,29);(1,3,4,2)(6,12)(11,24)(13,26)(14,21)(15,28)(25,35)(27,33)(29,36);(5,8)(6,13)(7,16)(9,20)(10,19)(11,25)(12,26)(14,27)(15,29)(17,31)(18,30)(21,33)(22,34)(23,32)(24,35)(28,36);(8,19)(13,26)(16,30)(20,32)(25,35)(27,33)(29,36)(31,34)5494 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 53163);