Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C83 · Schur multiplier (H2) = C24×C4 |
| direct product | C83×#18459 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C83 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C83 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C83 ◁ C2×C42×C83 ◁ G | |
972 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 2656 |
A minimal faithful permutation representation — 4 generators on 115 points:
(2,7)(3,11)(4,15)(8,21)(9,19)(10,16)(12,14)(13,28)(17,30)(20,25)(22,32)(23,29)(24,31)(26,27)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115);(1,2,5,10)(3,8,12,22)(4,16,15,7)(6,9,18,24)(11,25,14,23)(13,29,27,20)(17,31,30,19)(21,26,32,28);(3,12)(4,17)(7,19)(8,22)(11,14)(13,26)(15,30)(16,31)(20,21)(23,25)(27,28)(29,32);(1,3,6,14)(2,8,9,23)(4,13,17,28)(5,12,18,11)(7,20,19,32)(10,22,24,25)(15,27,30,26)(16,29,31,21)2822 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 11447);