Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#73005 |
| Fitting | C5×#399 ⋊ D3 |
| derived | #95⋊C3 ⋊ C22×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | #857⋊C2 |
| commutator, cosocle, hypocenter | #95⋊C3 | C22×C5 |
| Frattini | C23 | C2×C5×S4 |
| Fitting | C5×#399 | D3 |
| socle | C23×C5 | C2×S4 |
| LCS | G ▷ #95⋊C3 | |
| UCS | C1 ◁ C2×C5 | |
308 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,2,3,4,5)(6,12,13)(7,11,9)(14,15,25,18,20,23)(16,22,19)(17,21,24);(7,10)(8,12)(11,13)(15,19)(20,24)(21,23)(22,25)105 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236427);