Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24292 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C25 |
| direct product | C67×#25437 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C67 |
| prime radical | C2×AGL(1,ℤ/8)×C67 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C22×C4×C67 ◁ G | |
894 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 4 generators on 103 points:
(1,2,4,3)(5,6,10,16)(7,12,20,29)(8,21,24,32)(9,15,25,14)(11,19,27,18)(13,30,33,23)(17,34,22,26)(28,36,31,35)(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);(1,3,4,2)(5,7,9,18,10,20,25,19)(6,11,14,12,16,27,15,29)(8,17,23,35,24,22,30,36)(13,26,21,28,33,34,32,31);(2,3)(5,7)(6,12)(8,22)(9,18)(10,20)(11,15)(13,31)(14,27)(16,29)(17,24)(19,25)(21,26)(23,36)(28,33)(30,35)(32,34);(5,8,9,23,10,24,25,30)(6,13,14,21,16,33,15,32)(7,17,18,35,20,22,19,36)(11,26,12,28,27,34,29,31)2680 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 18425);