Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C27 |
| direct product | C73×#23434 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C73 | C2×#127 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| socle | C2×C73 | C2×#392 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C73 ◁ C23×C4×C73 ◁ G | |
1916 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)(3,12)(4,17)(5,22)(6,11)(7,10)(8,14)(9,20)(13,30)(15,24)(16,25)(18,29)(19,27)(21,28)(23,31)(26,32)(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)(2,8)(4,18)(5,15)(6,14)(7,16)(9,26)(10,24)(11,25)(12,22)(13,19)(17,23)(20,31)(21,32)(27,29)(28,30);(1,4)(2,9)(3,13)(5,19)(6,20)(7,21)(8,23)(10,27)(11,28)(12,29)(14,18)(15,32)(16,31)(17,22)(24,30)(25,26);(2,10)(8,24)(9,27)(11,22)(12,25)(17,28)(23,30)(26,29)3358 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 16422);