Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C83 · Schur multiplier (H2) = C28 |
| direct product | C83×#32896 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C83 | #2846 |
| commutator, Frattini, cosocle | C22×C4 | C24×C83 |
| prime radical | C83×H(7,𝔽2) | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C83 ◁ C22×C4×C83 ◁ G | |
3610 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 2656 |
A minimal faithful permutation representation — 4 generators on 115 points:
(1,2,7,13)(3,14,17,27)(4,10,19,26)(5,12,6,11)(8,20,24,16)(9,21,25,18)(15,22,32,29)(23,31,28,30)(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);(1,3)(2,8)(4,15)(5,20)(6,16)(7,17)(9,22)(10,23)(11,27)(12,14)(13,24)(18,31)(19,32)(21,30)(25,29)(26,28);(1,4)(2,9)(3,15)(5,18)(6,21)(7,19)(8,22)(10,11)(12,26)(13,25)(14,28)(16,30)(17,32)(20,31)(23,27)(24,29);(1,4)(2,10)(3,15)(5,21)(6,18)(7,19)(8,23)(9,11)(12,25)(13,26)(14,29)(16,31)(17,32)(20,30)(22,27)(24,28)3818 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 25884);