Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #85559 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C22×C4 |
| direct product | C5×#85559 |
| Fitting | C5×H(3,𝔽4) ⋊ D3 |
| derived | #5464 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #85559 |
| commutator, cosocle, hypocenter | #5464 | C2×C5 |
| Frattini | C22 | C5×#1020 |
| Fitting | C5×H(3,𝔽4) | D3 |
| socle | C22×C5 | #1020 |
| LCS | G ▷ #5464 | |
| UCS | C1 ◁ C5 | |
240 conjugacy classes of subgroups; only the 16 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 16 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,3,4,5)(6,7,19,8,10,12,18,16)(9,13,11,21,17,14,20,15);(7,8,11)(9,10,17)(12,21,19)(13,15,20)(14,16,18)60 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#11715753, D5×#85559, #72221439 |
| maximal normal subgroup of | C5×#11715753, D5×#85559, #72221439 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236995);