Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C73 · Schur multiplier (H2) = C27 |
| direct product | C2×C73×#1881 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C73 | #120 |
| commutator | C2×C4 | C23×C4×C73 |
| Frattini, cosocle | C22×C4 | C24×C73 |
| socle | C22×C73 | #386 |
| prime radical | C2×#575×C73 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C73 ◁ C23×C4×C73 ◁ G | |
1682 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)(5,14,17,25)(6,18)(7,12)(8,22)(9,13)(10,16,26,21)(11,19)(15,30,33,24)(20,27)(23,28)(29,31,34,32);(3,5,7,21,9,17,8,16)(4,10,12,25,13,26,22,14)(6,15,19,32,20,33,23,31)(11,24,27,34,28,30,18,29);(3,6)(4,11)(5,15)(7,19)(8,23)(9,20)(10,24)(12,27)(13,28)(14,29)(16,31)(17,33)(18,22)(21,32)(25,34)(26,30)4672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 13926);