Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C83 · Schur multiplier (H2) = C26 |
| direct product | C83×#24421 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C83 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C83 |
| prime radical | C83×#3585 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C83 ◁ C22×C4×C83 ◁ G | |
1310 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 2656 |
A minimal faithful permutation representation — 4 generators on 115 points:
(1,2,7,21,6,8,5,11)(3,12,20,9,15,23,13,22)(4,16,18,25,19,10,17,26)(14,27,28,31,29,32,30,24)(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);(2,8)(3,13)(5,7)(9,23)(10,16)(12,22)(14,28)(15,20)(17,18)(24,32)(27,31)(29,30);(1,3)(2,9)(4,14)(5,20)(6,15)(7,13)(8,22)(10,24)(11,23)(12,21)(16,31)(17,28)(18,30)(19,29)(25,27)(26,32);(1,4)(2,10)(3,14)(5,18)(6,19)(7,17)(8,16)(9,24)(11,26)(12,27)(13,28)(15,29)(20,30)(21,25)(22,31)(23,32)3320 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 17409);