Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C73 · Schur multiplier (H2) = C29 |
| direct product | C73×#61107 |
| 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 | |
2624 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)(3,12)(4,9)(5,21)(6,10)(7,15)(8,19)(11,22)(13,30)(14,29)(16,24)(17,25)(18,26)(20,27)(23,32)(28,31)(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);(1,3,6,17)(2,7,10,24)(4,13,20,32)(5,16,22,15)(8,23,26,30)(9,28,27,29)(11,25,21,12)(14,19,31,18);(1,4)(2,8)(3,13)(5,18)(6,20)(7,23)(9,21)(10,26)(11,27)(12,28)(14,16)(15,31)(17,32)(19,22)(24,30)(25,29);(1,4)(2,9)(3,14)(5,19)(6,20)(7,23)(8,21)(10,27)(11,26)(12,29)(13,16)(15,32)(17,31)(18,22)(24,30)(25,28);(2,10)(7,24)(8,26)(9,27)(11,21)(12,25)(23,30)(28,29)3796 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 54095);