Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C83 · Schur multiplier (H2) = C28 |
| direct product | C83×#61814 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C83 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C83 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C83 ◁ #532×C83 ◁ G | |
1688 conjugacy classes of subgroups.
| minimal degree | μ(G) = 131 |
| transitive degree | μt(G) = 10624 |
A minimal faithful permutation representation — 5 generators on 131 points:
(1,2)(3,9)(4,7)(5,8)(6,11)(10,15)(12,14)(13,16)(17,18,23,28)(19,24,32,42)(20,26,34,43)(21,27,22,37)(25,36,44,33)(29,45,30,39)(31,40,35,41)(38,46,48,47)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131);(1,3)(2,6)(4,10)(5,11)(7,13)(8,9)(12,16)(14,15)(17,19,23,32)(18,24,28,42)(20,29,34,30)(21,35,22,31)(25,38,44,48)(26,45,43,39)(27,41,37,40)(33,47,36,46);(1,4,5,12)(2,7,8,14)(3,10,11,16)(6,13,9,15)(17,20)(18,25)(19,29)(21,33)(22,36)(23,34)(24,38)(26,37)(27,43)(28,44)(30,32)(31,46)(35,47)(39,41)(40,45)(42,48);(3,11)(6,9)(10,16)(13,15)(17,20)(18,26)(19,30)(21,36)(22,33)(23,34)(24,39)(25,37)(27,44)(28,43)(29,32)(31,46)(35,47)(38,41)(40,48)(42,45);(2,8)(6,9)(7,14)(13,15)(17,21,23,22)(18,27,28,37)(19,31,32,35)(20,33,34,36)(24,40,42,41)(25,43,44,26)(29,46,30,47)(38,45,48,39)4067 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 54802);