Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C26 |
| direct product | C73×#33561 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C73 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C24×C73 |
| prime radical | C73×#3018 | C2 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C73 ◁ C2×C4×C73 ◁ C2×#41×C73 ◁ G | |
1096 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)(4,9)(5,10)(6,11)(7,12)(8,15)(14,25)(16,23)(17,22)(18,26)(19,27)(20,28)(21,29)(24,30)(31,32)(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);(1,3,7,4)(2,8,12,22)(5,16,19,14)(6,15,20,17)(9,11,13,28)(10,24,27,21)(18,30,31,29)(23,32,25,26);(1,4,7,3)(2,9,12,13)(5,14,19,16)(6,15,20,17)(8,11,22,28)(10,25,27,23)(18,30,31,29)(21,32,24,26);(1,5,7,19)(2,10,12,27)(3,14,4,16)(6,18,20,31)(8,21,22,24)(9,23,13,25)(11,26,28,32)(15,29,17,30)2482 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 26549);