Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C25 |
| direct product | C73×#23812 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C73 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| prime radical | C22×D8×C73 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C73 ◁ #376×C73 ◁ G | |
1022 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 9344 |
A minimal faithful permutation representation — 4 generators on 101 points:
(5,6,8,9)(7,10,11,12)(13,14,16,20,17,21,26,19)(15,22,24,27,23,28,25,18)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101);(1,2)(3,4)(6,9)(10,12)(13,15,17,23)(14,18,21,27)(16,25,26,24)(19,22,20,28);(2,4)(14,19)(16,26)(18,22)(20,21)(24,25)(27,28);(5,7,8,11)(6,10,9,12)(15,23)(18,27)(22,28)(24,25)3796 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 16800);