Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C83 · Schur multiplier (H2) = C25 |
| direct product | C83×#18407 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C83 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C83 |
| prime radical | C83×#3493 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C83 ◁ C2×C42×C83 ◁ G | |
904 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 5312 |
A minimal faithful permutation representation — 4 generators on 115 points:
(1,2)(3,9)(4,12)(5,7)(6,11)(8,14)(10,16)(13,15)(17,18,23,20)(19,26,30,32)(21,25,22,31)(24,28,27,29)(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)(2,6)(4,13)(5,10)(7,15)(8,16)(9,12)(11,14)(17,19)(18,24)(20,27)(21,29)(22,28)(23,30)(25,32)(26,31);(17,20,23,18)(19,27,30,24)(21,31,22,25)(26,28,32,29);(2,7)(3,10)(8,12)(11,13)(17,21,23,22)(18,25,20,31)(19,28,30,29)(24,26,27,32)3569 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 11395);