Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C83 · Schur multiplier (H2) = C2 |
| direct product | C83×#7463 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C83 | #367 |
| commutator | C16 | C2×C8×C83 |
| Frattini, cosocle | C4×C16 | C22×C83 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C83 ◁ C42×C83 ◁ C4×C8×C83 ◁ C4×C16×C83 ◁ G | |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 123 |
| transitive degree | μt(G) = 21248 |
A minimal faithful permutation representation — 2 generators on 123 points:
(1,2,3,5,4,6,7,8)(10,15,17,28)(11,20)(12,24)(13,25)(16,31)(18,32,35,40)(19,38,36,30)(21,26)(22,34)(23,33)(27,39,37,29)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123);(9,10,16,32,12,18,11,15,25,36,20,29,21,27,31,38,14,17,34,40,26,35,23,28,13,19,33,39,24,37,22,30)4316 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 451);