Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C73 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×C73×#1833 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C73 | #117 |
| commutator | C2×C4 | C23×C4×C73 |
| Frattini, cosocle | C22×C4 | C24×C73 |
| socle | C22×C73 | #382 |
| prime radical | C24×C73 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C73 ◁ C2×#117×C73 ◁ G | |
786 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 4 generators on 107 points:
(1,2)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(3,4)(5,13,16,9)(6,17,19,32)(7,12)(8,11)(10,18,23,33)(14,27)(15,26,30,22)(20,24)(21,28)(25,34)(29,31);(3,5,7,15,8,16,20,30)(4,9,12,22,11,13,24,26)(6,14,18,28,19,29,33,34)(10,21,17,31,23,25,32,27);(3,6)(4,10,11,23)(5,14)(7,18)(8,19)(9,21,13,25)(12,17,24,32)(15,28)(16,29)(20,33)(22,31,26,27)(30,34)4672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 13744);