Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C67 · Schur multiplier (H2) = C25 |
| direct product | C67×#22887 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C67 | C22×D4 |
| commutator | C2×C4 | C23×C4×C67 |
| Frattini, cosocle | C22×C4 | C24×C67 |
| socle | C22×C67 | C2×C4×D4 |
| prime radical | C67×#3002 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C67 ◁ C2×C22⋊C8×C67 ◁ G | |
1020 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 4 generators on 103 points:
(1,2)(3,4)(5,6,10,14,11,15,9,23)(7,16,18,12,19,27,24,28)(8,13,22,32,21,30,25,31)(17,33,35,26,34,29,20,36)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103);(5,7,10,18,11,19,9,24)(6,12,14,27,15,28,23,16)(8,20,22,17,21,35,25,34)(13,29,32,36,30,33,31,26);(2,4)(8,21)(13,30)(17,34)(20,35)(22,25)(26,36)(29,33)(31,32);(5,8)(6,13)(7,17)(9,25)(10,22)(11,21)(12,26)(14,32)(15,30)(16,33)(18,35)(19,34)(20,24)(23,31)(27,29)(28,36)3886 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 15875);