Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C83 · Schur multiplier (H2) = C27 |
| direct product | C83×#36670 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C83 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C83 |
| socle | C23×C83 | C25 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C83 ◁ G | |
1794 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 10624 |
A minimal faithful permutation representation — 5 generators on 115 points:
(1,2,4,6)(3,5,7,8)(9,10)(11,13)(12,14)(15,16)(17,18)(19,23)(20,24)(21,22)(25,28)(26,30)(27,29)(31,32)(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);(1,3,4,7)(2,5,6,8)(11,15)(13,16)(18,22)(23,28)(24,29)(30,32);(2,6)(5,8)(9,11)(10,13)(12,15)(14,16)(17,19)(18,23)(20,26)(21,25)(22,28)(24,30)(27,31)(29,32);(10,14)(11,15)(19,25)(23,28)(26,31)(30,32);(17,20,21,27)(18,24,22,29)(19,26,25,31)(23,30,28,32)4316 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 29658);