Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C2×C8 | S5 |
| commutator, hypocenter | SL(2,𝔽5) | C42 |
| Frattini | C2×C4 | C2×S5 |
| socle | C22 | C4×S5 |
| prime radical, cosocle | C2×#6732 | C22 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2×C8 | |
288 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Permutation generators:
(1,27,2,28)(3,35,16,29,20,42,7,46,25,33,10,51,4,36,15,30,19,41,8,45,26,34,9,52)(5,43,11,31,23,37,13,49,21,39,18,47,6,44,12,32,24,38,14,50,22,40,17,48);(1,27,2,28)(3,37,5,43,26,46)(4,38,6,44,25,45)(7,47,13,49,16,36)(8,48,14,50,15,35)(9,30,22,32,24,51)(10,29,21,31,23,52)(11,40,17,41,20,34)(12,39,18,42,19,33)96 conjugacy classes — view the full character table.
| maximal subgroup of | #72277090 |
| maximal normal subgroup of | #72277090 |
| maximal quotient of | C8×GL(2,𝔽5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240620);