Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C83 · Schur multiplier (H2) = C23×C4 |
| direct product | C83×#10867 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C83 | #117 |
| commutator | C2×C4 | C2×C42×C83 |
| Frattini, cosocle | C23×C4 | C23×C83 |
| socle | C22×C83 | #380 |
| prime radical | C24×C83 | C2×Q8 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C83 ◁ C22×M16×C83 ◁ G | |
714 conjugacy classes of subgroups.
| minimal degree | μ(G) = 119 |
| transitive degree | μt(G) = 5312 |
A minimal faithful permutation representation — 3 generators on 119 points:
(5,6,10,15,11,14,9,24)(7,16,18,27,19,12,25,28)(8,20,22,29,23,35,21,13)(17,31,32,30,33,34,36,26)(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)(6,12)(8,17)(9,18)(10,25)(11,19)(13,26)(14,16)(15,27)(20,34)(21,32)(22,36)(23,33)(24,28)(29,30)(31,35);(5,8,9,21,11,23,10,22)(6,13,15,20,14,29,24,35)(7,17,18,32,19,33,25,36)(12,26,27,34,16,30,28,31)5312 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 3855);