Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C4⋊C4 ⋊ S5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×S5 |
| commutator | C2×A5 | C22×C4 |
| Fitting, hypercenter | C4⋊C4 | S5 |
| socle, cosocle | C22×A5 | C23 |
| prime radical | C22×S5 | C22 |
| hypocenter | A5 | #117 |
| LCS | G ▷ C2×A5 ▷ A5 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
607 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 607 conjugacy classes of subgroups — too many to draw. Only its 41 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)(2,3,5)(6,11,8,13)(7,10,9,12)(14,19,16,21)(15,18,17,20)(22,27,24,29)(23,26,25,28)(30,35,32,37)(31,34,33,36);(1,5)(2,4)(6,32,9,31)(7,33,8,30)(10,36,13,35)(11,37,12,34)(14,22,17,25)(15,23,16,24)(18,26,21,29)(19,27,20,28);(1,4,3)(2,5)(6,17)(7,16)(8,15)(9,14)(10,21)(11,20)(12,19)(13,18)(22,33)(23,32)(24,31)(25,30)(26,37)(27,36)(28,35)(29,34)70 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240493);