Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C73 · Schur multiplier (H2) = C29 |
| direct product | C73×#61106 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C73 | C2×D42 |
| commutator, Frattini, cosocle | C2×C4 | C25×C73 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C73 ◁ C22×C4×C73 ◁ G | |
2656 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 5 generators on 105 points:
(1,2)(3,14)(4,10)(5,13)(6,12)(7,11)(8,17)(9,19)(15,23)(16,30)(18,29)(20,28)(21,25)(22,26)(24,32)(27,31)(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)(2,8)(4,15)(5,21)(6,17)(7,18)(9,23)(10,27)(11,25)(12,29)(13,14)(16,19)(20,32)(22,31)(24,26)(28,30);(1,4)(2,9)(3,15)(5,19)(6,22)(7,20)(8,23)(10,12)(11,26)(13,28)(14,30)(16,21)(17,31)(18,32)(24,25)(27,29);(1,4)(2,10)(3,16)(5,22)(6,19)(7,20)(8,24)(9,12)(11,28)(13,26)(14,30)(15,21)(17,32)(18,31)(23,25)(27,29);(2,11)(8,25)(9,26)(10,28)(12,13)(14,29)(23,24)(27,30)3796 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 54094);