Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C67 · Schur multiplier (H2) = C28 |
| direct product | C67×#60191 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C67 | C24 |
| commutator | C22 | C24×C4×C67 |
| Frattini, cosocle | C2×C4 | C25×C67 |
| socle | C22×C67 | C24×C4 |
| prime radical | C24×C67 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C67 ◁ G | |
1810 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 5 generators on 107 points:
(1,2)(3,8)(4,6)(5,7)(9,10,13,18,14,17,24,30)(11,15,21,27,20,26,33,37)(12,16,22,29,23,28,34,38)(19,25,32,36,31,35,39,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(1,3,5,4)(2,6,7,8)(9,11)(10,15)(12,19)(13,21)(14,20)(16,25)(17,26)(18,27)(22,32)(23,31)(24,33)(28,35)(29,36)(30,37)(34,39)(38,40);(1,4,5,3)(2,6,7,8)(9,12,13,22,14,23,24,34)(10,16,18,29,17,28,30,38)(11,19,21,32,20,31,33,39)(15,25,27,36,26,35,37,40);(11,20)(15,26)(19,31)(21,33)(25,35)(27,37)(32,39)(36,40);(10,17)(15,26)(16,28)(18,30)(25,35)(27,37)(29,38)(36,40)5896 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 53179);