Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C25 |
| direct product | C2×C73×#2097 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C73 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C73 ◁ C22×C42×C73 ◁ G | |
1150 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 18688 |
A minimal faithful permutation representation — 4 generators on 103 points:
(1,2)(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);(7,8,10,12)(9,13,14,11)(15,16,18,22,19,23,27,20)(17,24,25,29,26,30,28,21);(3,4)(5,6)(7,9,10,14)(8,11,12,13)(16,20)(18,27)(21,24)(22,23)(25,28)(29,30);(4,6)(15,17,19,26)(16,21,23,29)(18,28,27,25)(20,24,22,30)4672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 16717);