Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C83 · Schur multiplier (H2) = C23 |
| direct product | C83×#7178 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C83 | #102 |
| commutator | C8 | C4×C8×C83 |
| Frattini, cosocle | C2×C4×C8 | C22×C83 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C83 ◁ C2×C42×C83 ◁ C2×C4×C8×C83 ◁ G | |
274 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 21248 |
A minimal faithful permutation representation — 2 generators on 111 points:
(1,2)(3,4)(5,6,8,11,9,12,7,10)(14,19,20,23)(15,16)(17,25)(21,28,27,22)(24,26)(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);(2,4)(6,10,12,11)(13,14,16,21,25,28,15,23,18,20,26,27,17,22,24,19)5312 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 166);