Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C24 |
| direct product | C67×#33889 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C67 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C4×D4×C67 ◁ C8×D4×C67 ◁ G | |
574 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 4 generators on 107 points:
(1,2,4,6)(3,7,8,5)(9,10)(11,15)(12,16)(13,26)(14,17)(18,23)(19,24)(20,28)(21,31)(22,38)(25,32)(27,34)(29,37)(30,35)(33,39)(36,40)(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)(2,5)(4,8)(6,7)(9,11)(10,15)(12,21)(13,22)(14,20)(16,31)(17,28)(18,29)(19,30)(23,37)(24,35)(25,34)(26,38)(27,32)(33,40)(36,39);(10,16)(11,20)(12,23)(13,24)(15,27)(17,32)(18,19)(21,36)(25,39)(26,33)(28,31)(29,38)(30,40)(34,37);(3,8)(5,7)(10,17)(15,28)(16,32)(18,33)(19,26)(27,31)(29,40)(30,38)2881 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 26877);