Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C83 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×C83×#1515 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C83 | C2×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C83 |
| Frattini, cosocle | C22×C4 | C24×C83 |
| prime radical | C24×C83 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C83 ◁ C22×C42×C83 ◁ G | |
1022 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 5312 |
A minimal faithful permutation representation — 4 generators on 117 points:
(1,2)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117);(3,4)(5,11,13,8)(6,9)(7,10)(12,17,18,15)(14,16)(19,20)(21,27)(22,30)(23,25)(24,28)(26,32)(29,34)(31,33);(3,5,7,13)(4,8,10,11)(6,12,14,18)(9,15,16,17)(19,21,23,29)(20,24,25,33)(22,31,32,28)(26,34,30,27);(3,6,7,14)(4,9,10,16)(5,12,13,18)(8,15,11,17)(20,25)(24,33)(26,30)(27,34)4316 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 10545);