Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18930 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18961 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C11×#121 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
818 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11)(14,21)(15,16)(18,25)(19,23)(22,24)(26,27)(28,29,33,37)(30,38,41,51)(31,35,42,49)(32,44,46,36)(34,45,48,40)(39,52,53,59)(43,56,55,50)(47,57,58,54);(12,13)(14,18)(15,19)(16,23)(17,20)(21,26)(22,27)(24,25)(28,30,33,41)(29,34,37,48)(31,39,42,53)(32,45,46,40)(35,47,49,58)(36,51,44,38)(43,57,55,54)(50,59,56,52);(12,14)(13,18)(15,21)(16,24)(17,22)(19,26)(20,27)(23,25)(28,31,33,42)(29,35,37,49)(30,39,41,53)(32,43,46,55)(34,47,48,58)(36,50,44,56)(38,52,51,59)(40,54,45,57);(12,15,17,16)(13,19,20,23)(14,21,22,24)(18,26,27,25)(31,42)(35,49)(39,53)(43,55)(47,58)(50,56)(52,59)(54,57)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11949);