Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2184 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#2189 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C17 |
| prime radical | C2×C17×#135 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C22×C8×C17 ◁ G | |
220 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23,28,32)(24,33,36,51)(25,30,27,42)(26,38,41,52)(29,44,47,35)(31,37,49,40)(34,50,43,48)(39,45,53,46);(22,24)(23,29)(25,34)(26,39)(27,43)(28,36)(30,45)(31,48)(32,47)(33,38)(35,40)(37,44)(41,53)(42,46)(49,50)(51,52);(19,21)(22,25,28,27)(23,30,32,42)(24,34,36,43)(26,37,41,40)(29,45,47,46)(31,38,49,52)(33,50,51,48)(35,39,44,53)493 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 921);