Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C67 · Schur multiplier (H2) = C23×C4 |
| direct product | C67×#21290 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C67 | C22×D4 |
| commutator | C2×C4 | C23×C4×C67 |
| Frattini, cosocle | C22×C4 | C24×C67 |
| prime radical | C22×D8×C67 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C67 ◁ #376×C67 ◁ G | |
862 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 4 generators on 95 points:
(1,2,4,3)(5,6)(7,10)(8,9)(11,12)(14,18)(15,21)(17,23)(19,26)(22,28)(24,27)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95);(1,3,4,2)(6,9)(10,12)(13,14)(15,19)(16,18)(17,20)(21,27)(22,24)(23,25)(26,28);(13,15,17,21,16,22,23,28)(14,19,20,27,18,24,25,26);(5,7,8,11)(6,10,9,12)(14,18)(15,22)(20,25)(21,28)4288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 14278);