Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2048 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C67 · Schur multiplier (H2) = C25 |
| direct product | C67×#11119 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C67 | #394 |
| commutator | C22×C4 | C22×C4×C67 |
| Frattini, cosocle | C23×C4 | C23×C67 |
| socle | C2×C67 | #1439 |
| prime radical | C22×#41×C67 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C67 ◁ C23×C4×C67 ◁ G | |
864 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 2144 |
A minimal faithful permutation representation — 3 generators on 99 points:
(1,2)(3,13)(4,17,20,9)(5,12)(6,10)(7,11)(8,15)(14,29,31,25)(16,27)(18,32,30,23)(19,26,22,28)(21,24)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(1,3,5,15,7,16,6,21)(2,8,10,13,11,24,12,27)(4,18,19,14,20,30,22,31)(9,25,26,23,17,29,28,32);(1,4)(2,9)(3,14)(5,19)(6,22)(7,20)(8,23)(10,26)(11,17)(12,28)(13,29)(15,30)(16,31)(18,21)(24,32)(25,27)3082 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 4107);