Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×Q8 ⋊ S5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×S5 |
| commutator, socle, cosocle | C2×A5 | C24 |
| Fitting, hypercenter | C2×Q8 | S5 |
| hypocenter | A5 | 2−1+4 |
| LCS | G ▷ C2×A5 ▷ A5 | |
| UCS | C1 ◁ C2 ◁ C2×Q8 | |
1293 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 1293 conjugacy classes of subgroups — too many to draw. Only its 85 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:
(1,3,5,4)(6,11,7,10)(8,13,9,12)(14,19,15,18)(16,21,17,20)(22,27,23,26)(24,29,25,28)(30,35,31,34)(32,37,33,36);(1,5,3)(2,4)(6,20,7,21)(8,18,9,19)(10,16,11,17)(12,14,13,15)(22,36,23,37)(24,34,25,35)(26,32,27,33)(28,30,29,31);(1,4,2)(6,31)(7,30)(8,32)(9,33)(10,34)(11,35)(12,37)(13,36)(14,23)(15,22)(16,24)(17,25)(18,26)(19,27)(20,29)(21,28);(1,2)(6,15,7,14)(8,17,9,16)(10,18,11,19)(12,20,13,21)(22,31,23,30)(24,33,25,32)(26,34,27,35)(28,36,29,37)61 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240607);