Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16×C67 · Schur multiplier (H2) = C22 |
| direct product | C67×SD16⋊C16 |
| unambiguous semidirect product | SD16⋊(C16×C67) |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C67 | C2×D4 |
| commutator | C4 | C22×C16×C67 |
| Frattini, cosocle | C4×C8 | C23×C67 |
| socle | C22×C67 | C8×D4 |
| prime radical | C2×D4×C67 | C2×C8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C67 ◁ C4×C16×C67 ◁ G | |
232 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 3 generators on 91 points:
(1,2)(3,5)(4,6)(7,8)(9,10,12,16,13,17,20,23,14,11,15,18,21,19,22,24)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91);(2,5)(3,8)(6,7);(2,6)(5,7)(9,11,12,18,13,19,20,24,14,10,15,16,21,17,22,23)5896 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 5043);