Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C83 · Schur multiplier (H2) = C23 |
| direct product | C83×#12947 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C83 | #447 |
| commutator | C2×C8 | C22×C4×C83 |
| Frattini, cosocle | C22×C8 | C23×C83 |
| socle | C2×C83 | #1862 |
| prime radical | C2×#135×C83 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C83 ◁ C22×C4×C83 ◁ #405×C83 ◁ G | |
380 conjugacy classes of subgroups.
| minimal degree | μ(G) = 147 |
| transitive degree | μt(G) = 5312 |
A minimal faithful permutation representation — 3 generators on 147 points:
(1,2,7,14,9,15,8,30)(3,16,20,46,21,47,31,34)(4,22,25,43,26,58,32,38)(5,13,27,42,28,44,6,12)(10,19,35,54,37,56,36,18)(11,23,39,60,41,29,40,24)(17,48,51,62,53,63,52,33)(45,55,61,59,64,49,57,50)(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147);(1,3,7,20,9,21,8,31)(2,10,14,35,15,37,30,36)(4,17,25,51,26,53,32,52)(5,19,27,54,28,56,6,18)(11,33,39,48,41,62,40,63)(12,34,13,16,42,46,44,47)(22,57,43,45,58,61,38,64)(23,59,60,49,29,50,24,55);(1,4)(2,11)(3,17)(5,24)(6,29)(7,25)(8,32)(9,26)(10,33)(12,22)(13,43)(14,39)(15,41)(16,45)(18,50)(19,55)(20,51)(21,53)(23,27)(28,60)(30,40)(31,52)(34,57)(35,48)(36,63)(37,62)(38,44)(42,58)(46,61)(47,64)(49,56)(54,59)3818 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 5935);