Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C67 · Schur multiplier (H2) = C23×C4 |
| direct product | C67×#10871 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C67 | #121 |
| commutator | C2×C4 | C2×C42×C67 |
| Frattini, cosocle | C23×C4 | C23×C67 |
| socle | C22×C67 | #390 |
| prime radical | C24×C67 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C67 ◁ C23×C4×C67 ◁ G | |
746 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 3 generators on 103 points:
(1,2,3,4)(5,6)(7,16)(8,21)(9,25)(10,14)(11,15)(12,18)(13,22)(17,26)(19,28)(20,27)(23,29)(24,35)(30,32)(31,34)(33,36)(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);(5,7,10,18,11,20,9,19)(6,12,14,27,15,28,25,16)(8,17,23,31,24,33,22,32)(13,26,21,34,29,36,35,30);(5,8,9,22,11,24,10,23)(6,13,14,21,15,29,25,35)(7,17,19,32,20,33,18,31)(12,26,27,34,28,36,16,30)4288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 3859);