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×#21250 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C2×#121 |
| commutator | C2×C4 | C23×C4×C67 |
| Frattini, cosocle | C22×C4 | C24×C67 |
| prime radical | C22×#41×C67 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C23×C4×C67 ◁ G | |
1434 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)(5,6,10,15,11,14,9,23)(7,12,18,27,17,28,24,26)(8,19,22,29,20,33,21,13)(16,30,32,25,31,36,34,35)(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)(5,7,9,18,11,17,10,24)(6,12,15,26,14,28,23,27)(8,16,21,32,20,31,22,34)(13,25,19,30,29,35,33,36);(5,8,9,21,11,20,10,22)(6,13,15,19,14,29,23,33)(7,16,18,32,17,31,24,34)(12,25,26,30,28,35,27,36);(8,20)(13,29)(16,31)(19,33)(21,22)(25,35)(30,36)(32,34)3886 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 14238);