Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C83 · Schur multiplier (H2) = C25 |
| direct product | C83×#17684 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C83 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C83 |
| Frattini, cosocle | C42 | C24×C83 |
| prime radical | C83×#3517 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C83 ◁ C4×#41×C83 ◁ G | |
932 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 10624 |
A minimal faithful permutation representation — 4 generators on 115 points:
(1,2,6,11,7,10,5,9)(3,12,13,16,4,8,14,15)(17,18)(19,25,27,32)(20,24)(21,23)(22,26,30,28)(29,31)(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);(1,3,7,4)(2,8,10,12)(5,13,6,14)(9,15,11,16)(17,19)(18,22)(20,28)(21,27)(23,30)(24,32)(25,31)(26,29);(1,4,7,3)(2,8,10,12)(5,13,6,14)(9,16,11,15)(18,23)(22,30)(24,31)(25,32);(1,5,7,6)(2,9,10,11)(3,13,4,14)(8,15,12,16)4067 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 10672);