Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C83 · Schur multiplier (H2) = C26 |
| direct product | C83×#21777 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C83 | #2308 |
| commutator | C23 | C23×C4×C83 |
| Frattini, cosocle | C24 | C24×C83 |
| prime radical | C83×#3485 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C83 ◁ C24×C83 ◁ G | |
1318 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)(3,11,14,7)(4,8)(5,17,18,9)(6,10)(12,19,26,21)(13,20)(15,28,29,22)(16,23)(24,27)(25,31)(30,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115);(1,3)(2,7)(4,12)(5,13)(6,14)(8,21)(9,20)(10,11)(15,25)(16,26)(17,24)(18,27)(19,23)(22,31)(28,30)(29,32);(1,4,6,16)(2,8,10,23)(3,12,14,26)(5,15,18,29)(7,19,11,21)(9,22,17,28)(13,25,27,32)(20,30,24,31);(1,5)(2,9)(3,13)(4,15)(6,18)(7,20)(8,22)(10,17)(11,24)(12,25)(14,27)(16,29)(19,30)(21,31)(23,28)(26,32)3818 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 14765);