Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C83 · Schur multiplier (H2) = C2 |
| direct product | C83×#7098 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C83 | #331 |
| commutator | C4×C8 | C2×C4×C83 |
| Frattini, cosocle | C82 | C22×C83 |
| LCS | G ▷ C4×C8 ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C83 ◁ C42×C83 ◁ C82×C83 ◁ G | |
142 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 21248 |
A minimal faithful permutation representation — 2 generators on 115 points:
(1,2,3,8,4,7,11,15,5,9,12,16,13,6,10,14)(18,22)(19,25)(20,27)(23,32)(24,31)(26,29)(28,30)(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);(2,6)(3,10)(4,13)(7,9)(8,16)(11,12)(17,18,21,24)(19,26,28,32)(20,29,27,23)(22,30,31,25)3569 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 86);