Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C83 · Schur multiplier (H2) = C4 |
| direct product | C83×#9585 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C83 | #121 |
| commutator | C42 | C22×C4×C83 |
| Frattini, cosocle | C2×C42 | C23×C83 |
| socle | C22×C83 | #388 |
| prime radical | C23×C83 | #126 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C83 ◁ C2×C42×C83 ◁ G | |
290 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 10624 |
A minimal faithful permutation representation — 3 generators on 115 points:
(2,6)(3,9)(4,11)(7,14)(8,13)(12,15)(17,18,21,25,22,26,20,23)(19,27,29,24,30,31,28,32)(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);(1,2,4,6,5,8,11,13)(3,7,10,12,9,15,16,14)(18,23,26,25)(24,27,32,31);(1,3,4,10,5,9,11,16)(2,7,6,12,8,15,13,14)(17,19,20,28,22,30,21,29)(18,24,25,31,26,32,23,27)4814 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 2573);