Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C83 · Schur multiplier (H2) = C26 |
| direct product | C83×#21781 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C83 | #2308 |
| commutator | C23 | C23×C4×C83 |
| Frattini, cosocle | C22×C4 | C24×C83 |
| prime radical | C83×#3487 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C83 ◁ C22×C4×C83 ◁ G | |
1258 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 2656 |
A minimal faithful permutation representation — 4 generators on 115 points:
(1,2,6,12,7,11,4,9)(3,13,14,22,16,8,20,24)(5,18,17,26,19,10,21,25)(15,23,30,31,29,27,28,32)(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)(2,8)(4,14)(5,15)(6,20)(7,16)(9,24)(10,23)(11,13)(12,22)(17,28)(18,27)(19,29)(21,30)(25,32)(26,31);(1,4,7,6)(2,9,11,12)(3,14,16,20)(5,17,19,21)(8,22,13,24)(10,25,18,26)(15,28,29,30)(23,31,27,32);(1,5,7,19)(2,10,11,18)(3,15,16,29)(4,17,6,21)(8,23,13,27)(9,25,12,26)(14,28,20,30)(22,31,24,32)3818 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 14769);