Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C83 · Schur multiplier (H2) = C24 |
| direct product | C83×#11319 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C83 | #401 |
| commutator | C24 | C22×C4×C83 |
| Frattini, cosocle | C23×C4 | C23×C83 |
| socle | C2×C83 | #1443 |
| prime radical | C24×C83 | C22×C4 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C83 ◁ C23×C4×C83 ◁ G | |
532 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 2656 |
A minimal faithful permutation representation — 3 generators on 115 points:
(1,2,5,10,6,9,18,25)(3,7,13,21,12,20,17,26)(4,14,16,29,15,8,22,24)(11,19,28,31,27,23,30,32)(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)(2,7,9,20)(4,11,15,27)(5,17)(6,12)(8,23)(10,26,25,21)(13,18)(14,19)(16,30,22,28)(24,31)(29,32);(1,4)(2,8,9,14)(3,11,12,27)(5,16)(6,15)(7,19)(10,24,25,29)(13,28,17,30)(18,22)(20,23)(21,31)(26,32)3818 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 4307);