Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23892 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C27 |
| direct product | C67×#23894 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C67 | #2403 |
| commutator, Frattini, cosocle | C22×C4 | C24×C67 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C67 ◁ C22×C4×C67 ◁ G | |
1642 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 2144 |
A minimal faithful permutation representation — 4 generators on 99 points:
(1,2,7,12)(3,13,18,26)(4,19,22,29)(5,23,6,11)(8,17,27,16)(9,20,10,21)(14,30,31,24)(15,25,32,28)(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);(1,3)(2,8)(4,15)(5,17)(6,16)(7,18)(9,28)(10,25)(11,26)(12,27)(13,23)(14,20)(19,24)(21,31)(22,32)(29,30);(1,4)(2,9)(3,14)(5,20)(6,21)(7,22)(8,24)(10,12)(11,29)(13,25)(15,16)(17,32)(18,31)(19,23)(26,28)(27,30);(1,4)(2,10)(3,15)(5,21)(6,20)(7,22)(8,25)(9,12)(11,29)(13,24)(14,16)(17,31)(18,32)(19,23)(26,30)(27,28)2680 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 16882);