Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3055 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C67 · Schur multiplier (H2) = C27×C4 |
| direct product | C2×C67×#3139 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C67 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C67 |
| prime radical | C24×C67 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C67 ◁ C22×C42×C67 ◁ G | |
2118 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 5 generators on 93 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(3,4)(5,8)(6,7)(9,10)(11,12,17,22)(13,19,23,26)(14,18,24,25)(15,21,16,20);(4,7)(8,10)(11,13,16,24,17,23,15,14)(12,18,21,26,22,25,20,19);(3,5,6,9)(4,8,7,10)(11,14,15,23,17,24,16,13)(12,19,20,25,22,26,21,18);(13,23)(14,24)(18,25)(19,26)4288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 53602);