Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C83 · Schur multiplier (H2) = C25 |
| direct product | C83×#17524 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C83 | C22×D4 |
| commutator | C2×C4 | C23×C4×C83 |
| Frattini, cosocle | C42 | C24×C83 |
| socle | C22×C83 | C22×C22⋊C4 |
| prime radical | C83×#3482 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C83 ◁ C4×#41×C83 ◁ G | |
936 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 10624 |
A minimal faithful permutation representation — 4 generators on 115 points:
(2,6)(3,9)(4,11)(7,14)(8,12)(13,15)(17,18,21,25,22,24,20,29)(19,26,27,23,28,32,30,31)(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);(1,2,5,8)(3,7,9,15)(4,12,11,6)(10,14,16,13)(17,19,22,28)(18,23,24,31)(20,30,21,27)(25,32,29,26);(1,3)(2,7)(4,10)(5,9)(6,13)(8,15)(11,16)(12,14)(18,24)(23,31)(25,29)(26,32);(3,9)(7,15)(10,16)(13,14)4814 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 10512);