Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C83 · Schur multiplier (H2) = C28 |
| direct product | C83×#62164 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C83 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C83 |
| prime radical | C83×#3519 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C83 ◁ #529×C83 ◁ G | |
1758 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 5312 |
A minimal faithful permutation representation — 5 generators on 115 points:
(1,2,5,8)(3,9,10,6)(4,12,13,7)(11,14,16,15)(17,18)(19,26)(20,24)(21,23)(22,27)(25,29)(28,31)(30,32)(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);(1,3)(2,6)(4,11)(5,10)(7,14)(8,9)(12,15)(13,16)(17,19)(18,22)(20,27)(21,28)(23,30)(24,26)(25,31)(29,32);(18,23)(21,29)(22,30)(24,25)(26,31)(28,32);(3,10)(6,9)(11,16)(14,15)(19,27)(22,26)(28,32)(30,31);(1,4,5,13)(2,7,8,12)(3,11,10,16)(6,14,9,15)(18,24)(19,27)(23,25)(28,32)4067 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 55152);