Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61609 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#61925 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| prime radical | C11×#3224 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#533 ◁ G | |
1664 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 5 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,22)(15,19)(16,20)(17,21)(18,24)(23,27)(25,26)(28,29,33,38)(30,40,42,35)(31,44,46,53)(32,39,34,37)(36,48,51,45)(41,55,56,59)(43,50,47,52)(49,58,54,57);(12,14,17,24)(13,18,21,22)(15,23,16,25)(19,26,20,27)(28,30,33,42)(29,35,38,40)(31,41,46,56)(32,47,34,43)(36,49,51,54)(37,52,39,50)(44,59,53,55)(45,58,48,57);(12,15,17,16)(13,19,21,20)(14,23,24,25)(18,26,22,27)(28,31,33,46)(29,36,38,51)(30,41,42,56)(32,45,34,48)(35,49,40,54)(37,44,39,53)(43,57,47,58)(50,55,52,59);(12,16,17,15)(13,20,21,19)(14,23,24,25)(18,26,22,27)(30,42)(35,40)(41,56)(43,47)(49,54)(50,52)(55,59)(57,58);(13,21)(18,22)(19,20)(26,27)(28,32,33,34)(29,37,38,39)(30,43,42,47)(31,45,46,48)(35,50,40,52)(36,44,51,53)(41,57,56,58)(49,55,54,59)539 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54913);