Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C83 · Schur multiplier (H2) = C23×C42 |
| direct product | C2×C83×#1747 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C83 | C42 |
| commutator | C4 | C22×C42×C83 |
| Frattini, cosocle | C22×C4 | C24×C83 |
| socle | C22×C83 | #376 |
| prime radical | C24×C83 | #41 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C83 ◁ G | |
930 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 5312 |
A minimal faithful permutation representation — 4 generators on 117 points:
(1,2)(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);(3,4)(5,13,16,26)(6,10)(7,11)(8,12)(9,15,21,29)(14,25,28,33)(17,22)(18,23)(19,24)(20,27,31,34)(30,32);(3,5)(4,9,12,21)(6,14)(7,15)(8,16)(10,20,23,31)(11,13,24,26)(17,27)(18,28)(19,29)(22,25,32,33)(30,34);(3,6,7,17,8,18,19,30)(4,10,11,22,12,23,24,32)(5,14,15,27,16,28,29,34)(9,20,13,25,21,31,26,33)7304 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 13357);