Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C23×C4 |
| direct product | C73×#19726 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C73 |
| prime radical | C73×#3184 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G | |
724 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 9344 |
A minimal faithful permutation representation — 4 generators on 105 points:
(1,2,7,4)(3,10,14,16)(5,9,6,15)(8,12,11,13)(17,18,23,28)(19,25,30,31)(20,24,29,32)(21,26,22,27)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105);(1,3,5,12,7,14,6,13)(2,8,15,16,4,11,9,10)(17,19,22,29,23,30,21,20)(18,24,26,31,28,32,27,25);(1,4,7,2)(3,11,14,8)(5,9,6,15)(10,13,16,12)(17,20,21,30,23,29,22,19)(18,25,27,32,28,31,26,24);(1,5,7,6)(2,9,4,15)(3,12,14,13)(8,10,11,16)(17,21,23,22)(18,26,28,27)(19,29,30,20)(24,25,32,31)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 12714);