Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C26 |
| direct product | C73×#33571 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C73 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×Q8 | C24×C73 |
| prime radical | C73×#3018 | C2 |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C73 ◁ C2×C4×C73 ◁ C2×#41×C73 ◁ G | |
1084 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)(3,13)(4,10)(5,19)(6,9)(7,12)(8,15)(11,22)(14,25)(16,29)(17,28)(18,26)(20,27)(21,30)(23,32)(24,31)(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);(1,3,7,17)(2,8,12,25)(4,15,5,14)(6,21,22,16)(9,23,11,24)(10,28,19,13)(18,31,20,32)(26,30,27,29);(2,9)(6,22)(8,23)(10,26)(11,12)(13,29)(16,21)(18,20)(19,27)(24,25)(28,30)(31,32);(1,4,7,5)(2,10,12,19)(3,14,17,15)(6,18,22,20)(8,13,25,28)(9,26,11,27)(16,31,21,32)(23,29,24,30)2482 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 26559);