Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C83 · Schur multiplier (H2) = C23 |
| direct product | C83×#12944 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C83 | #447 |
| commutator | C2×C8 | C22×C4×C83 |
| Frattini, cosocle | C22×C8 | C23×C83 |
| socle | C2×C83 | #1862 |
| prime radical | C2×#135×C83 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C83 ◁ C22×C4×C83 ◁ C2×#97×C83 ◁ G | |
388 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 2656 |
A minimal faithful permutation representation — 3 generators on 115 points:
(1,2,6,12,8,13,7,26)(3,14,18,30,19,10,23,29)(4,20,17,28,21,27,16,9)(5,22,15,31,25,32,24,11)(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);(1,3,6,18,8,19,7,23)(2,9,12,20,13,28,26,27)(4,15,17,25,21,24,16,5)(10,11,29,22,14,31,30,32);(1,4)(2,10)(3,15)(5,23)(6,17)(7,16)(8,21)(9,11)(12,29)(13,14)(18,25)(19,24)(20,22)(26,30)(27,32)(28,31)3320 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 5932);