Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 6 |
| isoclinism | isoclinic class of #7548 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×#7548 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #1424 |
| commutator | C32 | C2×C4×C11 |
| Frattini, cosocle | C2×C32 | C22×C11 |
| prime radical | C22×C11 | SD64 |
| LCS | G ▷ C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C2×C8×C11 ◁ C2×C11×C16 ◁ C2×C11×C32 ◁ G | |
62 conjugacy classes of subgroups.
| minimal degree | μ(G) = 75 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 2 generators on 75 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,19,21,37)(14,25)(15,30)(16,31)(17,34)(20,41)(22,50,47,64)(23,54,48,74)(24,55,49,40)(26,33)(27,44)(28,46)(29,45)(32,59)(35,62)(36,63,52,38)(39,67,66,51)(42,69,70,65)(43,72)(53,75,73,71)(56,57)(58,68)(60,61);(12,13,20,42,15,22,43,66,31,51,58,64,61,69,29,37,17,24,45,63,32,53,68,74,35,48,72,75,26,36,41,55,18,21,46,70,33,47,27,39,62,67,57,50,59,65,14,19,34,49,25,38,60,73,56,54,16,23,44,71,30,52,28,40)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 536);