Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#13551 |
| subgroup | G/H | |
|---|---|---|
| center | C11×C16 | C42 |
| commutator | C4 | C2×C4×C8×C11 |
| Frattini, cosocle | C2×C16 | C23×C11 |
| socle | C2×C11 | C2×#346 |
| prime radical | C23×C11 | M32 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C11×C16 ◁ G | |
214 conjugacy classes of subgroups.
| minimal degree | μ(G) = 75 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 75 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,20,16,22,30,42,17,23,31,43,33,46,57,68,18,21,32,41,34,44,58,66,35,45,59,67,60,69,74,75)(14,24,26,48,27,49,52,71,28,37,53,40,54,63,72,65,25,47,29,55,50,70,56,73,51,19,36,38,61,39,62,64);(12,14)(13,19,21,37)(15,29)(16,27)(17,28)(18,25)(20,40,41,38)(22,39,44,63)(23,24,45,47)(26,32)(30,56)(31,36)(33,54)(34,50)(35,51)(42,65,66,64)(43,55,67,48)(46,49,69,70)(52,58)(53,59)(57,62)(60,61)(68,73,75,71)(72,74);(14,25)(19,37)(24,47)(26,29)(27,50)(28,51)(36,53)(38,40)(39,63)(48,55)(49,70)(52,56)(54,61)(62,72)(64,65)(71,73)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6539);