Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C83 · Schur multiplier (H2) = C28 |
| direct product | C2×C83×#3119 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C83 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C83 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C83 ◁ C2×#117×C83 ◁ G | |
2198 conjugacy classes of subgroups.
| minimal degree | μ(G) = 109 |
| transitive degree | μt(G) = 10624 |
A minimal faithful permutation representation — 5 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);(3,4)(5,8)(6,7)(9,10)(11,12)(13,16)(14,17)(15,19)(18,22)(20,24)(21,23)(25,26);(4,7)(8,10)(11,13,15,20)(12,16,19,24)(14,21,22,26)(17,23,18,25);(12,17)(14,22)(16,23)(18,19)(21,26)(24,25);(3,5,6,9)(4,8,7,10)(13,20)(16,24)(21,26)(23,25)5312 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 53536);