Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C73 · Schur multiplier (H2) = C23 |
| direct product | C73×#11924 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C73 | #102 |
| commutator | C2×C8 | C22×C4×C73 |
| Frattini, cosocle | C4×C8 | C23×C73 |
| socle | C22×C73 | C2×#102 |
| prime radical | C73×#3147 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C73 ◁ C2×C42×C73 ◁ C2×C4×C8×C73 ◁ G | |
414 conjugacy classes of subgroups.
| minimal degree | μ(G) = 113 |
| transitive degree | μt(G) = 9344 |
A minimal faithful permutation representation — 3 generators on 113 points:
(1,2,3,6,4,5,7,8)(9,10)(11,21,24,37)(12,17)(13,27)(14,19)(15,20)(16,23,32,40)(18,29)(22,34,25,38)(26,36)(28,31,39,33)(30,35)(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);(2,5)(3,7)(9,11)(10,16)(12,22)(13,28)(14,25)(15,24)(17,31)(18,34)(19,33)(20,32)(21,35)(23,26)(27,37)(29,40)(30,39)(36,38);(9,12,15,14)(10,17,20,19)(11,22,24,25)(13,26,30,29)(16,31,32,33)(18,27,36,35)(21,34,37,38)(23,39,40,28)4234 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 4912);