Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42×C83 · Schur multiplier (H2) = C28×C4 |
| direct product | C83×#60058 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C83 | C24 |
| commutator | C2 | C23×C42×C83 |
| Frattini, cosocle | C2×C4 | C25×C83 |
| socle | C22×C83 | C24×C4 |
| prime radical | C22×#41×C83 | C22 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C83 ◁ G | |
3178 conjugacy classes of subgroups.
| minimal degree | μ(G) = 119 |
| transitive degree | μt(G) = 5312 |
A minimal faithful permutation representation — 5 generators on 119 points:
(5,6,9,13,10,14,20,26)(7,11,17,23,16,22,29,33)(8,12,19,25,18,24,30,34)(15,21,28,32,27,31,35,36)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119);(1,2,3,4)(5,7)(6,11)(8,15)(9,17)(10,16)(12,21)(13,23)(14,22)(18,27)(19,28)(20,29)(24,31)(25,32)(26,33)(30,35)(34,36);(5,8)(6,12)(7,15)(9,19)(10,18)(11,21)(13,25)(14,24)(16,27)(17,28)(20,30)(22,31)(23,32)(26,34)(29,35)(33,36);(8,18)(12,24)(15,27)(19,30)(21,31)(25,34)(28,35)(32,36);(7,16)(11,22)(15,27)(17,29)(21,31)(23,33)(28,35)(32,36)11288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 53046);