Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33522 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#33588 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C2×C11×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#117 ◁ C11×#405 ◁ G | |
680 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 79 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(16,17,22,27)(18,23,29,44)(19,32,35,66)(20,36,40,65)(21,41,38,26)(24,47,49,33)(25,50,52,39)(28,54,55,77)(30,60,58,76)(31,63,59,46)(34,67,42,51)(37,53,68,48)(43,69,70,56)(45,73,72,62)(57,78,64,74)(61,75,79,71);(12,13,14,15)(16,18)(17,23)(19,28)(20,30)(21,31)(22,29)(24,43)(25,45)(26,46)(27,44)(32,54)(33,56)(34,57)(35,55)(36,60)(37,61)(38,59)(39,62)(40,58)(41,63)(42,64)(47,69)(48,71)(49,70)(50,73)(51,74)(52,72)(53,75)(65,76)(66,77)(67,78)(68,79);(16,19,22,35)(17,24,27,49)(18,28,29,55)(20,37,40,68)(21,42,38,34)(23,43,44,70)(25,51,52,67)(26,53,41,48)(30,61,58,79)(31,64,59,57)(32,65,66,36)(33,50,47,39)(45,74,72,78)(46,75,63,71)(54,76,77,60)(56,73,69,62);(18,29)(23,44)(28,55)(30,58)(31,59)(43,70)(45,72)(46,63)(54,77)(56,69)(57,64)(60,76)(61,79)(62,73)(71,75)(74,78)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26576);