Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C24 |
| direct product | C2×C73×#2229 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C73 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C73 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C73 ◁ C2×C42×C73 ◁ C2×C4×C8×C73 ◁ G | |
542 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 18688 |
A minimal faithful permutation representation — 4 generators on 115 points:
(1,2)(43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115);(3,4,6,8)(5,9,10,7)(11,12,14,17)(13,21,22,39)(15,27,25,40)(16,30,26,20)(18,34,32,23)(19,36,33,29)(24,41,31,37)(28,38,42,35);(3,5,6,10)(4,7,8,9)(12,17)(18,32)(19,33)(20,30)(21,39)(27,40)(35,38)(37,41);(11,13,14,22)(12,18,17,32)(15,28,25,42)(16,31,26,24)(19,37,33,41)(20,38,30,35)(21,40,39,27)(23,36,34,29)4234 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 26613);