Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C83 · Schur multiplier (H2) = C25 |
| direct product | C2×C83×#1657 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C83 | #120 |
| commutator, Frattini, cosocle | C42 | C24×C83 |
| prime radical | C2×#496×C83 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C83 ◁ C2×C42×C83 ◁ G | |
1010 conjugacy classes of subgroups.
| minimal degree | μ(G) = 109 |
| transitive degree | μt(G) = 10624 |
A minimal faithful permutation representation — 4 generators on 109 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109);(4,7)(5,9)(8,10)(12,17)(13,20)(14,15)(19,22)(21,23)(24,25);(5,9)(7,10)(11,12)(13,18)(14,22)(15,17)(16,19)(20,25)(21,26)(23,24);(3,4)(5,10)(6,8)(7,9)(11,13,16,21)(12,18,19,26)(14,20,15,23)(17,24,22,25)3320 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 11970);