Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32941 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C24×C4 |
| direct product | C67×#33192 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C67 |
| prime radical | C2×#472×C67 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C2×C42×C67 ◁ G | |
998 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 4 generators on 103 points:
(2,4)(5,6)(7,17)(8,22)(9,16)(10,13)(11,15)(12,19)(14,23)(18,32)(20,28)(21,26)(24,30)(25,29)(27,34)(31,33)(35,36)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103);(5,7,9,19,10,20,11,21)(6,12,15,17,13,26,16,28)(8,18,23,33,24,34,25,35)(14,27,22,31,29,32,30,36);(1,2,3,4)(6,13)(12,26)(14,29)(15,16)(17,28)(22,30)(27,32)(31,36);(5,8)(6,14)(7,18)(9,23)(10,24)(11,25)(12,27)(13,29)(15,22)(16,30)(17,31)(19,33)(20,34)(21,35)(26,32)(28,36)3484 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 26180);