Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C27×C4 |
| direct product | C11×#60819 |
| 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 ◁ C4×C11×#41 ◁ G | |
2058 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)(22,31)(23,35)(24,29)(25,27)(26,32)(28,36)(30,38)(33,40)(34,39)(37,43)(41,46)(42,48)(44,45)(47,50)(49,51);(12,14,15,19)(13,16,17,18)(20,22)(21,26)(23,33)(24,32)(25,34)(27,41)(28,40)(29,31)(30,39)(35,44)(36,45)(37,47)(38,46)(42,50)(43,49)(48,51);(14,19)(16,18)(21,27)(22,32)(25,38)(26,39)(28,42)(29,30)(31,41)(33,45)(35,43)(37,48)(40,49)(44,50);(13,17)(16,18)(20,23)(21,28)(22,33)(24,36)(25,37)(26,40)(27,42)(29,35)(30,43)(31,44)(32,45)(34,47)(38,48)(39,49)(41,50)(46,51);(23,36)(28,35)(33,45)(37,48)(40,44)(42,43)(47,51)(49,50)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53807);