Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C67 · Schur multiplier (H2) = C22×C4 |
| direct product | C67×#8184 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C8×C67 | D4 |
| commutator | C4 | C2×C4×C8×C67 |
| Frattini, cosocle | C2×C42 | C23×C67 |
| socle | C22×C67 | C4×C22⋊C4 |
| prime radical | C2×#41×C67 | C2×C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C8×C67 ◁ C2×C4×C8×C67 ◁ G | |
530 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 3 generators on 91 points:
(9,10,13,17,14,18,12,15)(11,16,20,23,21,24,19,22)(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);(1,2,3,5,4,6,7,8)(10,15,18,17)(16,22,24,23);(9,11,13,20,14,21,12,19)(10,16,17,23,18,24,15,22)7504 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 1172);