Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C83 · Schur multiplier (H2) = C213 |
| direct product | C2×C83×#3458 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C83 | C24 |
| commutator, Frattini, cosocle | C22 | C26×C83 |
| socle | C23×C83 | C25 |
| prime radical | C25×C83 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C83 ◁ G | |
7022 conjugacy classes of subgroups.
| minimal degree | μ(G) = 109 |
| transitive degree | μt(G) = 5312 |
A minimal faithful permutation representation — 6 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);(3,4,6,8)(5,9,10,7)(11,12)(13,19)(14,18)(15,17)(16,20)(21,25)(22,24)(23,26);(11,13)(12,16)(14,21)(15,20)(17,19)(18,23)(22,26)(24,25);(3,5,6,10)(4,7,8,9)(13,20)(16,19)(21,26)(23,25);(12,17)(16,19)(18,24)(23,25);(11,14,15,22)(12,18,17,24)(13,21,20,26)(16,23,19,25)7304 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 55672);