Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C73 · Schur multiplier (H2) = C25 |
| direct product | C73×#23043 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C73 | D42 |
| commutator | C2×C4 | C23×C4×C73 |
| Frattini, cosocle | C22×C4 | C24×C73 |
| socle | C2×C73 | #2361 |
| prime radical | C73×#3067 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C73 ◁ C22×C4×C73 ◁ G | |
820 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 4 generators on 105 points:
(1,2,7,12)(3,13)(4,5,22,25)(6,10,14,11)(8,18)(9,20,24,21)(15,26)(16,32)(17,28)(19,29)(23,27)(30,31)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105);(1,3,14,17,7,19,6,18)(2,8,11,13,12,28,10,29)(4,15,21,31,22,32,20,27)(5,23,9,26,25,30,24,16);(1,4)(2,9)(3,15)(5,10)(6,20)(7,22)(8,26)(11,25)(12,24)(13,30)(14,21)(16,28)(17,31)(18,27)(19,32)(23,29);(1,5,6,24,7,25,14,9)(2,4,10,20,12,22,11,21)(3,16,17,23,19,26,18,30)(8,27,13,15,28,31,29,32)3796 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 16031);