Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2230 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C67 · Schur multiplier (H2) = C23 |
| direct product | C67×#12950 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | #476 |
| commutator | C2×C8 | C22×C4×C67 |
| Frattini, cosocle | C22×C8 | C23×C67 |
| prime radical | C2×#135×C67 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C22×C4×C67 ◁ C2×C4×C8×C67 ◁ G | |
412 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 3 generators on 87 points:
(1,2)(3,4)(6,12,14,7)(8,18)(9,19)(10,20)(13,15,17,16)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87);(2,4)(5,6,10,16,11,14,20,15)(7,8,13,18,12,19,17,9);(5,7)(6,8)(9,15)(10,13)(11,12)(14,19)(16,18)(17,20)3082 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 5938);