Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C73 · Schur multiplier (H2) = C25×C4 |
| direct product | C73×#21220 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C73 |
| Frattini, cosocle | C22×C4 | C24×C73 |
| prime radical | C22×#41×C73 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C2×#117×C73 ◁ G | |
1454 conjugacy classes of subgroups.
| minimal degree | μ(G) = 109 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 4 generators on 109 points:
(2,4)(5,6,9,14,10,13,15,27)(7,11,18,23,17,24,21,28)(8,12,20,26,19,25,29,35)(16,22,31,34,30,33,32,36)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109);(5,7,15,18,10,17,9,21)(6,11,14,28,13,24,27,23)(8,16,29,31,19,30,20,32)(12,22,26,36,25,33,35,34);(1,2,3,4)(5,8)(6,12)(7,16)(9,20)(10,19)(11,22)(13,25)(14,26)(15,29)(17,30)(18,31)(21,32)(23,34)(24,33)(27,35)(28,36);(8,19)(12,25)(16,30)(20,29)(22,33)(26,35)(31,32)(34,36)4234 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 14208);