Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | Q16 ⋊ S5 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×S5 |
| commutator, cosocle | C4×A5 | C23 |
| Frattini | C4 | C22×S5 |
| Fitting, hypercenter | Q16 | S5 |
| socle | C2×A5 | C2×D4 |
| prime radical | #11756681 | C2 |
| hypocenter | A5 | #137 |
| LCS | G ▷ C4×A5 ▷ C2×A5 ▷ A5 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q16 | |
442 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 27 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
Permutation generators:
(1,2)(3,5,4)(6,15,7,14)(8,16,9,17)(10,19,11,18)(12,20,13,21)(22,31,23,30)(24,32,25,33)(26,35,27,34)(28,36,29,37);(2,5,4,3)(6,10)(7,11)(8,12)(9,13)(14,18)(15,19)(16,20)(17,21)(22,26)(23,27)(24,28)(25,29)(30,34)(31,35)(32,36)(33,37);(1,4,5,2,3)(6,26,7,27)(8,29,9,28)(10,23,11,22)(12,24,13,25)(14,36,15,37)(16,34,17,35)(18,33,19,32)(20,31,21,30)40 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240587);