Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C24 |
| direct product | C2×C73×#2090 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C73 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| prime radical | C24×C73 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C73 ◁ C23×C4×C73 ◁ G | |
810 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 9344 |
A minimal faithful permutation representation — 4 generators on 99 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(3,4)(5,10)(6,8)(7,9)(11,12,15,18,16,20,14,19)(13,17,21,26,23,24,22,25);(3,5,7,6)(4,8,9,10)(11,13)(12,17)(14,22)(15,21)(16,23)(18,26)(19,25)(20,24);(3,6,7,5)(4,8,9,10)(12,18)(13,21)(14,15)(17,24)(19,20)(22,23)3796 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 16661);