Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2031 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C67 · Schur multiplier (H2) = C26 |
| direct product | C67×#11038 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C67 | #124 |
| commutator | C22×C4 | C22×C4×C67 |
| Frattini, cosocle | C23×C4 | C23×C67 |
| socle | C22×C67 | #394 |
| prime radical | C2×#575×C67 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C67 ◁ C23×C4×C67 ◁ G | |
1278 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 3 generators on 103 points:
(1,2)(3,4)(5,6)(7,17)(8,22,25,13)(9,16)(10,14)(11,15)(12,19)(18,30,33,35)(20,28)(21,29)(23,27,34,36)(24,31,26,32)(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);(2,4)(5,7)(6,12)(8,23)(9,21)(10,19)(11,20)(13,30)(14,28)(15,29)(16,17)(18,24)(22,35)(25,34)(26,33)(27,31)(32,36);(5,8)(6,13)(7,18)(9,24)(10,26)(11,25)(12,27)(14,31)(15,22)(16,32)(17,30)(19,23)(20,33)(21,34)(28,35)(29,36)3484 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 4026);