Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C67 · Schur multiplier (H2) = C25×C4 |
| direct product | C67×#21248 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C67 | #121 |
| commutator | C2×C4 | C23×C4×C67 |
| Frattini, cosocle | C22×C4 | C24×C67 |
| socle | C22×C67 | C2×#121 |
| prime radical | C22×#135×C67 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C67 ◁ C23×C4×C67 ◁ G | |
1458 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)(5,6,10,16,11,15,9,14)(7,12,18,26,19,28,24,27)(8,20,22,30,23,29,21,13)(17,31,32,25,33,35,34,36)(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);(1,2,3,4)(5,7,10,24,11,19,9,18)(6,12,14,26,15,28,16,27)(8,17,22,34,23,33,21,32)(13,25,29,35,30,36,20,31);(5,8,9,21,11,23,10,22)(6,13,16,20,15,30,14,29)(7,17,18,32,19,33,24,34)(12,25,27,31,28,36,26,35);(5,9,11,10)(6,14,15,16)(7,18,19,24)(8,21,23,22)(12,26,28,27)(13,29,30,20)(17,32,33,34)(25,35,36,31)4288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 14236);