Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C83 · Schur multiplier (H2) = C26 |
| direct product | C83×#22462 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C83 | D42 |
| commutator | C2×C4 | C23×C4×C83 |
| Frattini, cosocle | C22×C4 | C24×C83 |
| socle | C2×C83 | D4×C22⋊C4 |
| prime radical | C83×#3584 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C83 ◁ C22×C4×C83 ◁ G | |
1320 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 2656 |
A minimal faithful permutation representation — 4 generators on 115 points:
(1,2,7,11)(3,12,16,14)(4,17)(5,20,6,10)(8,21,24,15)(9,22)(13,28)(18,26)(19,25)(23,32)(27,30)(29,31)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115);(1,3)(2,8)(4,13)(5,21)(6,15)(7,16)(9,23)(10,14)(11,24)(12,20)(17,27)(18,31)(19,32)(22,30)(25,29)(26,28);(1,4)(2,9)(3,13)(5,18)(6,22)(7,19)(8,23)(10,25)(11,26)(12,27)(14,29)(15,30)(16,32)(17,20)(21,31)(24,28);(1,2)(3,14)(4,9)(5,20)(6,10)(7,11)(8,21)(12,16)(13,29)(15,24)(17,18)(19,26)(22,25)(23,31)(27,32)(28,30)4814 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 15450);