Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C83 · Schur multiplier (H2) = C26 |
| direct product | C83×#24474 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C83 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C83 |
| prime radical | C83×#3586 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C83 ◁ C22×C4×C83 ◁ G | |
1298 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 2656 |
A minimal faithful permutation representation — 4 generators on 115 points:
(1,2,6,11,7,5,24,10)(3,12,16,14,17,26,15,8)(4,18,22,20,23,28,21,9)(13,25,30,32,31,29,19,27)(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);(1,3)(2,8)(4,19)(5,14)(6,16)(7,17)(9,27)(10,26)(11,12)(13,22)(15,24)(18,25)(20,32)(21,31)(23,30)(28,29);(1,4,7,23)(2,9,5,20)(3,13,17,31)(6,21,24,22)(8,25,14,29)(10,18,11,28)(12,27,26,32)(15,30,16,19);(1,5)(2,7)(3,14)(4,20)(6,10)(8,17)(9,23)(11,24)(12,15)(13,29)(16,26)(18,21)(19,32)(22,28)(25,31)(27,30)3320 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 17462);