Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #7855 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C67 · Schur multiplier (H2) = C23×C4 |
| direct product | C67×#10799 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C67 | C2×C42 |
| commutator | C2×C4 | C2×C42×C67 |
| Frattini, cosocle | C23×C4 | C23×C67 |
| socle | C22×C67 | #376 |
| prime radical | C24×C67 | #41 |
| LCS | G ▷ C2×C4 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C67 ◁ G | |
650 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)(7,15,18,28)(8,12)(9,13)(10,14)(11,17,23,31)(16,27,30,35)(19,24)(20,25)(21,26)(22,29,33,36)(32,34)(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);(5,7)(6,11,14,23)(8,16)(9,17)(10,18)(12,22,25,33)(13,15,26,28)(19,29)(20,30)(21,31)(24,27,34,35)(32,36);(2,4)(5,8,9,19,10,20,21,32)(6,12,13,24,14,25,26,34)(7,16,17,29,18,30,31,36)(11,22,15,27,23,33,28,35)4288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 3787);