Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C83 · Schur multiplier (H2) = C26 |
| direct product | C83×#10764 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C83 | C2×C22⋊C4 |
| commutator | C23 | C2×C42×C83 |
| Frattini, cosocle | C23×C4 | C23×C83 |
| socle | C22×C83 | C4×C22⋊C4 |
| prime radical | C22×#41×C83 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C83 ◁ C23×C8×C83 ◁ G | |
1194 conjugacy classes of subgroups.
| minimal degree | μ(G) = 119 |
| transitive degree | μt(G) = 5312 |
A minimal faithful permutation representation — 3 generators on 119 points:
(1,2)(3,4)(5,6)(7,15,17,11)(8,19,20,12)(9,14)(10,13)(16,23)(18,28,31,24)(21,32,33,25)(22,26)(27,30)(29,34)(35,36)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119);(2,4)(5,7,9,18,10,17,22,31)(6,11,14,24,13,15,26,28)(8,16,21,29,20,30,33,36)(12,23,25,34,19,27,32,35);(5,8)(6,12)(7,16)(9,21)(10,20)(11,23)(13,19)(14,25)(15,27)(17,30)(18,29)(22,33)(24,34)(26,32)(28,35)(31,36)5312 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 3752);