Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C83 · Schur multiplier (H2) = C25 |
| direct product | C83×#18416 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C83 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C83 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C83 ◁ C23×C4×C83 ◁ G | |
978 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)(4,14)(8,20)(9,18)(10,15)(12,24)(13,27)(16,29)(19,22)(21,31)(23,30)(25,26)(28,32)(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)(4,15,14,7)(6,9,17,23)(11,22,24,32)(13,28,26,19)(16,30,29,18)(20,25,31,27);(3,12)(4,16)(7,18)(8,21)(11,24)(13,27)(14,29)(15,30)(19,31)(20,28)(22,32)(25,26);(1,3)(2,8)(4,13)(5,12)(6,11)(7,19)(9,22)(10,21)(14,26)(15,28)(16,25)(17,24)(18,20)(23,32)(27,29)(30,31)3071 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 11404);