Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C73 · Schur multiplier (H2) = C24×C4 |
| direct product | C73×#17604 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C73 |
| Frattini, cosocle | C22×C4 | C24×C73 |
| prime radical | C73×#3494 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C2×#117×C73 ◁ G | |
1004 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 4 generators on 105 points:
(2,7,9,20)(4,15)(8,19,23,30)(10,21,11,16)(13,27)(17,29)(22,28,24,31)(25,32)(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);(1,2)(3,8)(4,16)(5,10)(6,11)(7,17)(9,18)(12,22)(13,28)(14,24)(15,20)(19,25)(21,29)(23,26)(27,30)(31,32);(1,3,5,14)(2,8,10,24)(4,13,15,27)(6,12,18,26)(7,19,21,31)(9,23,11,22)(16,28,20,30)(17,25,29,32);(3,12)(8,22)(13,25)(14,26)(19,28)(23,24)(27,32)(30,31)3796 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 10592);