Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13334 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#13335 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2011 |
| commutator, Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C11×#3414 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ C11×#405 ◁ G | |
536 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)(14,24)(15,29)(16,34)(17,40)(18,22)(19,26)(20,31)(21,38)(23,37)(25,43)(27,65)(28,57)(30,48)(32,70)(33,47)(35,53)(36,54)(39,55)(41,50)(42,51)(44,64)(45,71)(46,61)(49,69)(52,62)(56,59)(58,67)(60,75)(63,73)(66,74)(68,72);(12,14,18,28)(13,19,22,44)(15,25,33,61)(16,35,39,71)(17,41,37,27)(20,46,48,43)(21,50,52,65)(23,53,40,45)(24,55,57,34)(26,62,64,38)(29,67,47,56)(30,68,31,63)(32,66,42,60)(36,59,69,58)(49,74,54,75)(51,72,70,73);(12,15)(13,20)(14,25)(16,36)(17,42)(18,33)(19,43)(21,51)(22,48)(23,54)(24,56)(26,63)(27,66)(28,61)(29,34)(30,62)(31,38)(32,37)(35,59)(39,69)(40,49)(41,60)(44,46)(45,75)(47,55)(50,73)(52,70)(53,74)(57,67)(58,71)(64,68)(65,72)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6323);