Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C67 · Schur multiplier (H2) = C26 |
| direct product | C22×#359×C67 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C67 | D8 |
| commutator | C8 | C23×C4×C67 |
| Frattini, cosocle | C2×C8 | C24×C67 |
| socle | C23×C67 | #102 |
| prime radical | C22×#135×C67 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C67 ◁ C23×C4×C67 ◁ C23×C8×C67 ◁ G | |
1174 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 4 generators on 103 points:
(1,2)(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);(3,4);(5,6,9,14,11,15,10,25)(7,16,18,32,19,33,26,30)(8,20,22,31,24,35,23,13)(12,21,27,34,29,36,28,17);(5,7)(6,12)(8,21)(9,18)(10,26)(11,19)(13,30)(14,27)(15,29)(16,20)(17,23)(22,34)(24,36)(25,28)(31,32)(33,35)5896 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 26371);