Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C83 · Schur multiplier (H2) = C23 |
| direct product | C83×#10342 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C83 | #120 |
| commutator, Frattini, cosocle | C23×C4 | C23×C83 |
| prime radical | C24×C83 | C2×D4 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C83 ◁ C23×C4×C83 ◁ G | |
544 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 5312 |
A minimal faithful permutation representation — 3 generators on 115 points:
(1,2,4,6)(3,7,8,5)(9,10)(11,13)(12,15)(14,16)(17,18)(19,22)(20,23)(21,24)(25,30)(26,29)(27,31)(28,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115);(1,3,4,8)(2,5,6,7)(17,19)(18,22)(20,25)(21,26)(23,30)(24,29)(27,32)(28,31);(10,13)(11,16)(14,15)(17,20,21,27)(18,23,24,31)(19,25,26,32)(22,28,29,30)3320 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 3330);