Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C25 |
| direct product | C73×#33594 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C73 | #459 |
| commutator, Frattini, cosocle | C2×C8 | C24×C73 |
| socle | C2×C73 | C2×#459 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C73 ◁ C22×C4×C73 ◁ C2×C4×C8×C73 ◁ G | |
696 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)(5,11)(6,21)(7,22)(8,13)(9,15)(10,14)(16,29)(18,32)(19,28)(20,24)(23,25)(26,30)(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);(1,3,6,15,8,16,5,7)(2,9,11,12,13,22,21,29)(4,14,19,30,20,31,18,23)(10,24,25,28,27,17,26,32);(1,4)(2,10)(3,14)(5,18)(6,19)(7,23)(8,20)(9,24)(11,25)(12,28)(13,27)(15,30)(16,31)(17,22)(21,26)(29,32);(1,5,8,6)(2,11,13,21)(3,7,16,15)(4,18,20,19)(9,12,22,29)(10,25,27,26)(14,23,31,30)(17,32,24,28)3358 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 26582);