Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C83 · Schur multiplier (H2) = C24×C4 |
| direct product | C83×#18435 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C83 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C83 |
| prime radical | C83×#1600 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C83 ◁ C2×C42×C83 ◁ G | |
922 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 2656 |
A minimal faithful permutation representation — 4 generators on 115 points:
(2,7)(3,11)(4,15)(8,20)(9,18)(10,16)(12,24)(14,28)(17,27)(19,23)(21,31)(22,30)(25,26)(29,32)(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);(1,2,5,10)(3,8,12,21)(4,16,15,7)(6,9,13,22)(11,23,24,32)(14,29,26,19)(17,30,27,18)(20,25,31,28);(3,12)(4,17)(7,18)(8,21)(11,24)(14,28)(15,27)(16,30)(19,31)(20,29)(23,32)(25,26);(1,3,13,24)(2,8,22,32)(4,14,27,28)(5,12,6,11)(7,19,30,31)(9,23,10,21)(15,26,17,25)(16,29,18,20)3071 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 11423);