Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C67 · Schur multiplier (H2) = C28 |
| direct product | C2×C67×#2981 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C67 | C24 |
| commutator | C22 | C24×C4×C67 |
| Frattini, cosocle | C2×C4 | C25×C67 |
| socle | C23×C67 | C23×C4 |
| prime radical | C2×#532×C67 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C67 ◁ G | |
2230 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 5 generators on 93 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(3,4)(5,9)(6,8)(7,10)(11,12,15,19,14,18,22,26)(13,17,21,25,20,16,23,24);(3,5)(4,7)(6,10)(8,9)(11,13)(12,16)(14,20)(15,21)(17,18)(19,24)(22,23)(25,26);(5,10)(7,9)(11,13)(12,17)(14,20)(15,21)(16,18)(19,25)(22,23)(24,26);(4,8)(7,9)(12,18)(13,20)(19,26)(21,23)5896 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 53217);