Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61609 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#61681 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#532 ◁ G | |
2036 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 5 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,18)(15,17)(16,19)(20,21)(22,28)(23,34)(24,29)(25,38)(26,32)(27,36)(30,37)(31,46)(33,41)(35,45)(39,43)(40,50)(42,48)(44,49)(47,51);(12,14)(13,16)(15,19)(17,18)(20,22)(21,26)(23,31)(24,32)(25,33)(27,40)(28,29)(30,41)(34,51)(35,47)(36,48)(37,49)(38,44)(39,50)(42,43)(45,46);(20,23,24,35)(21,27,29,43)(22,31,32,47)(25,39,37,36)(26,40,28,42)(30,45,38,34)(33,50,49,48)(41,46,44,51);(14,19)(16,18)(20,22)(21,28)(23,31)(24,32)(25,33)(26,29)(27,42)(30,44)(34,46)(35,47)(36,48)(37,49)(38,41)(39,50)(40,43)(45,51);(13,17)(16,18)(21,29)(22,32)(27,43)(30,38)(31,47)(33,49)(34,45)(48,50)539 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54669);