Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C73 · Schur multiplier (H2) = C23 |
| direct product | C73×#11893 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C2×#102 |
| commutator | C2×C8 | C22×C4×C73 |
| Frattini, cosocle | C22×C8 | C23×C73 |
| prime radical | C73×#3050 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C23×C4×C73 ◁ C23×C8×C73 ◁ G | |
400 conjugacy classes of subgroups.
| minimal degree | μ(G) = 113 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 3 generators on 113 points:
(1,2)(3,7,8,5)(4,6)(9,10,13,19,15,21,14,20)(11,22,25,38,27,39,26,36)(12,28,30,18,32,37,31,17)(16,29,33,24,35,40,34,23)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113);(1,3)(2,5)(4,8)(6,7)(9,11)(10,16)(12,29)(13,26)(14,25)(15,27)(17,36)(18,38)(19,34)(20,33)(21,35)(22,37)(23,30)(24,31)(28,39)(32,40);(3,8)(5,7)(9,12,13,30,15,32,14,31)(10,17,20,37,21,18,19,28)(11,23,25,29,27,24,26,40)(16,22,34,36,35,39,33,38)3796 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 4881);