Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 6 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C83 · Schur multiplier (H2) = C2 |
| direct product | C83×#7541 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C83 | #1415 |
| commutator | C32 | C2×C4×C83 |
| Frattini, cosocle | C2×C32 | C22×C83 |
| prime radical | C2×D32×C83 | C2 |
| LCS | G ▷ C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C83 ◁ C2×C4×C83 ◁ C2×C8×C83 ◁ C2×C16×C83 ◁ C2×C32×C83 ◁ G | |
94 conjugacy classes of subgroups.
| minimal degree | μ(G) = 147 |
| transitive degree | μt(G) = 5312 |
A minimal faithful permutation representation — 2 generators on 147 points:
(1,2,4,11,8,14,7,32)(3,15,18,42,22,9,21,33)(5,25,23,58,29,38,28,60)(6,30,24,46,31,61,27,13)(10,36,39,16,41,49,62,19)(12,44,43,17,37,52,59,26)(20,55,50,35,57,45,53,48)(34,63,40,54,47,56,64,51)(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);(2,9)(3,16)(4,7)(5,26)(6,27)(10,37)(11,42)(12,41)(13,45)(14,15)(17,29)(18,36)(19,22)(20,56)(21,49)(23,52)(24,31)(25,34)(28,44)(30,35)(32,33)(38,47)(39,43)(40,60)(46,55)(48,61)(50,54)(51,53)(57,63)(58,64)(59,62)3818 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 529);