Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C83 · Schur multiplier (H2) = C29 |
| direct product | C2×C83×#2916 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C83 | C22×D4 |
| commutator | C4 | C24×C4×C83 |
| Frattini, cosocle | C2×C4 | C25×C83 |
| socle | C22×C83 | C22×C4⋊C4 |
| prime radical | C22×#41×C83 | C22 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C83 ◁ C22×#41×C83 ◁ G | |
2586 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 5312 |
A minimal faithful permutation representation — 5 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);(3,4,8,12,9,13,7,22)(5,14,17,24,18,28,16,10)(6,11,21,26,19,25,20,32)(15,27,31,33,29,34,30,23);(3,5,7,16,9,18,8,17)(4,10,12,14,13,24,22,28)(6,15,20,30,19,29,21,31)(11,23,26,27,25,33,32,34);(3,6)(4,11)(5,15)(7,20)(8,21)(9,19)(10,23)(12,26)(13,25)(14,27)(16,30)(17,31)(18,29)(22,32)(24,33)(28,34);(6,19)(11,25)(15,29)(20,21)(23,33)(26,32)(27,34)(30,31)7304 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 53100);