Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C83 · Schur multiplier (H2) = C23 |
| direct product | C2×C83×#1340 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C83 | #327 |
| commutator | C2×C8 | C22×C4×C83 |
| Frattini, cosocle | C2×M16 | C23×C83 |
| prime radical | C24×C83 | D8 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C83 ◁ C22×C4×C83 ◁ C22×M16×C83 ◁ G | |
444 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 5312 |
A minimal faithful permutation representation — 3 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)(5,14,16,31)(6,19,21,30)(7,12)(8,24)(9,13)(10,15)(11,22,28,23)(17,27,18,34)(20,29)(25,32)(26,33);(3,5,9,16)(4,10,13,26)(6,20,21,32)(7,18,8,17)(11,27,28,34)(12,29,24,25)(14,30,31,19)(15,22,33,23)3320 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 4672);