Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32947 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C26 |
| direct product | C67×#32947 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C67 | #2847 |
| commutator, Frattini, cosocle | C22×C4 | C24×C67 |
| prime radical | C67×#3027 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C67 ◁ C22×C4×C67 ◁ G | |
1306 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 2144 |
A minimal faithful permutation representation — 4 generators on 99 points:
(2,7)(5,16)(8,17)(9,18)(10,19)(11,23)(12,25)(14,26)(20,30)(21,28)(22,29)(27,31)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(1,2,5,7,6,10,16,19)(3,8,12,17,13,21,25,28)(4,9,14,18,15,22,26,29)(11,20,24,27,23,31,32,30);(1,3)(2,8)(4,11)(5,12)(6,13)(7,17)(9,20)(10,21)(14,24)(15,23)(16,25)(18,27)(19,28)(22,31)(26,32)(29,30);(1,4)(2,9)(3,11)(5,14)(6,15)(7,18)(8,20)(10,22)(12,24)(13,23)(16,26)(17,27)(19,29)(21,31)(25,32)(28,30)3082 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 25935);