Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C83 · Schur multiplier (H2) = C26 |
| direct product | C83×#21785 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C83 | #2308 |
| commutator | C2×C4 | C23×C4×C83 |
| Frattini, cosocle | C22×C4 | C24×C83 |
| prime radical | C83×#3500 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C83 ◁ C22×C4×C83 ◁ G | |
1262 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)(3,13,17,8)(4,10,5,19)(6,12)(7,11)(9,18,27,20)(14,30)(15,24)(16,29,21,25)(22,28)(23,31)(26,32)(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)(2,8)(4,14)(5,15)(6,21)(7,17)(9,26)(10,24)(11,13)(12,29)(16,22)(18,32)(19,30)(20,31)(23,27)(25,28);(1,4,7,5)(2,9,11,27)(3,14,17,15)(6,20,22,18)(8,23,13,26)(10,12,19,28)(16,32,21,31)(24,25,30,29);(1,5,7,4)(2,10,11,19)(3,15,17,14)(6,20,22,18)(8,24,13,30)(9,12,27,28)(16,32,21,31)(23,25,26,29)3818 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 14773);