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×#60823 |
| 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 | |
2054 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)(22,32)(23,38)(24,30)(25,31)(26,42)(27,36)(28,39)(29,40)(33,48)(34,44)(35,49)(37,45)(41,47)(43,51)(46,50);(12,14,15,19)(13,16,17,18)(20,22)(21,27)(23,34)(24,35)(25,36)(26,37)(28,46)(29,44)(30,45)(31,32)(33,40)(38,48)(39,51)(41,50)(42,49)(43,47);(14,19)(16,18)(20,23)(21,28)(22,33)(24,39)(25,40)(26,41)(27,43)(29,30)(31,47)(32,46)(34,36)(35,50)(37,51)(38,42)(44,49)(45,48);(13,17)(16,18)(20,23)(21,29)(22,34)(24,41)(25,40)(26,39)(27,44)(28,30)(31,38)(32,48)(33,36)(35,50)(37,51)(42,47)(43,49)(45,46);(20,24,25,26)(21,30,31,42)(22,35,36,37)(23,39,40,41)(27,45,32,49)(28,29,47,38)(33,50,34,51)(43,48,46,44)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53811);