Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C67 · Schur multiplier (H2) = C28 |
| direct product | C67×#36699 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C67 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C67 |
| socle | C23×C67 | C25 |
| prime radical | C2×#121×C67 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C67 ◁ G | |
1958 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 5 generators on 103 points:
(1,2,3,4)(5,6)(7,11)(8,12)(9,10)(13,16)(14,18)(15,17)(19,20)(21,22,25,28)(23,26,30,34)(24,27,32,36)(29,33,31,35)(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);(6,10)(11,16)(12,17)(18,20)(21,23,25,30)(22,26,28,34)(24,31,32,29)(27,35,36,33);(2,4)(5,7)(6,11)(8,14)(9,13)(10,16)(12,18)(15,19)(17,20)(21,24)(22,27)(23,29)(25,32)(26,33)(28,36)(30,31)(34,35);(7,13)(11,16)(14,19)(18,20)(22,28)(24,32)(26,34)(29,31);(5,8,9,15)(6,12,10,17)(7,14,13,19)(11,18,16,20)3484 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 29687);