Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C83 · Schur multiplier (H2) = C24 |
| direct product | C83×#11366 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C83 | #121 |
| commutator | C22×C4 | C22×C4×C83 |
| Frattini, cosocle | C23×C4 | C23×C83 |
| prime radical | C24×C83 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C83 ◁ C23×C4×C83 ◁ G | |
634 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 10624 |
A minimal faithful permutation representation — 3 generators on 111 points:
(5,6)(7,12)(8,10)(9,11)(13,14,17,22,18,20,16,21)(15,23,24,27,26,19,25,28)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111);(1,2)(3,4)(5,7,9,8)(6,10,11,12)(13,15,18,26)(14,19,20,23)(16,24,17,25)(21,28,22,27);(2,4)(5,8,9,7)(6,10,11,12)(14,20)(15,24)(16,17)(19,27)(23,28)(25,26)4316 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 4354);