Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×S5 |
| commutator | C2×A5 | C22×C4 |
| Frattini | C22 | C22×S5 |
| Fitting, hypercenter | C22×C4 | S5 |
| socle, cosocle | C22×A5 | C23 |
| prime radical | C23×A5 | C22 |
| hypocenter | A5 | #117 |
| LCS | G ▷ C2×A5 ▷ A5 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 | |
741 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 741 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Permutation generators:
(1,4)(2,5)(6,21,8,19)(7,20,9,18)(10,15,12,17)(11,14,13,16)(22,37,24,35)(23,36,25,34)(26,31,28,33)(27,30,29,32);(1,5,2)(3,4)(6,22,7,23)(8,24,9,25)(10,26,11,27)(12,28,13,29)(14,32,15,33)(16,30,17,31)(18,36,19,37)(20,34,21,35);(1,4,2,5)(6,31,9,32)(7,30,8,33)(10,35,13,36)(11,34,12,37)(14,25,17,22)(15,24,16,23)(18,29,21,26)(19,28,20,27)76 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240490);