Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C83 · Schur multiplier (H2) = C24 |
| direct product | C83×#17881 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C83 | C22×D4 |
| commutator | C2×C4 | C23×C4×C83 |
| Frattini, cosocle | C42 | C24×C83 |
| socle | C22×C83 | C2×C4×D4 |
| prime radical | C2×#135×C83 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C83 ◁ #431×C83 ◁ G | |
660 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 10624 |
A minimal faithful permutation representation — 4 generators on 107 points:
(1,2,4,3,5,6,8,7)(9,10)(11,16)(12,18)(13,17)(14,19)(15,20)(21,24)(22,23)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(9,11)(10,15)(12,20)(13,22)(14,21)(16,17)(18,24)(19,23);(1,3,4,6,5,7,8,2)(9,11)(10,16)(12,22)(13,20)(14,21)(15,17)(18,23)(19,24);(9,12,14,13)(10,17,19,18)(11,20,21,22)(15,16,23,24)5312 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 10869);