Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C25×C4 |
| direct product | C73×#25798 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C73 | #2433 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C73 ◁ C22×C4×C73 ◁ G | |
1430 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 4 generators on 105 points:
(1,2)(3,11)(4,16)(5,19)(6,10)(7,14)(8,17)(9,20)(12,25)(13,26)(15,24)(18,29)(21,28)(22,30)(23,27)(31,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105);(1,3,5,14,6,15,20,25)(2,7,9,11,10,12,19,24)(4,13,17,27,18,28,30,32)(8,21,16,23,22,26,29,31);(1,2)(3,12,15,7)(4,8)(5,9)(6,10)(11,14,24,25)(13,26,28,21)(16,17)(18,22)(19,20)(23,27,31,32)(29,30);(1,4,5,17,6,18,20,30)(2,8,9,16,10,22,19,29)(3,13,14,27,15,28,25,32)(7,21,11,23,12,26,24,31)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 18786);