Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C25 |
| direct product | C2×C73×#2212 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | #459 |
| commutator, Frattini, cosocle | C2×C8 | C24×C73 |
| prime radical | C2×#509×C73 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C22×C4×C73 ◁ C2×C4×C8×C73 ◁ G | |
706 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)(6,18)(7,22)(8,24)(9,14)(10,16)(11,15)(12,23)(17,31)(19,30)(20,34)(21,26)(25,27)(28,32)(29,33);(3,5,7,16,9,17,23,8)(4,10,12,13,14,24,22,31)(6,15,19,32,21,33,20,25)(11,26,27,30,29,18,28,34);(3,6)(4,11)(5,15)(7,19)(8,25)(9,21)(10,26)(12,27)(13,30)(14,29)(16,32)(17,33)(18,24)(20,23)(22,28)(31,34)3358 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 26579);