Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C83 · Schur multiplier (H2) = C26 |
| direct product | C83×#22456 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C83 | D4×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C83 |
| Frattini, cosocle | C22×C4 | C24×C83 |
| prime radical | C2×#577×C83 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C83 ◁ C22×C4×C83 ◁ G | |
1336 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 2656 |
A minimal faithful permutation representation — 4 generators on 115 points:
(1,2)(3,11)(4,16,18,8)(5,19)(6,10)(7,14)(9,20)(12,26,29,25)(13,23)(15,22)(17,24,32,31)(21,28,30,27)(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);(1,3,6,15)(2,7,10,23)(4,12,18,29)(5,13,20,14)(8,21,16,30)(9,22,19,11)(17,27,32,28)(24,26,31,25);(1,4)(2,8)(3,12)(5,17)(6,18)(7,21)(9,24)(10,16)(11,25)(13,27)(14,28)(15,29)(19,31)(20,32)(22,26)(23,30);(3,13)(5,20)(7,22)(9,19)(11,23)(12,27)(14,15)(17,32)(21,26)(24,31)(25,30)(28,29)4316 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 15444);