Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #4625⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#4625⋊C2 |
| unambiguous semidirect product | #4625⋊(C2×C5) |
| unambiguous semidirect product | (#1020⋊C2)⋊(C2×C5) |
| unambiguous semidirect product | #5450⋊(C2×C5) |
| Fitting | C5×H(3,𝔽4) ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #4625⋊C2 |
| commutator, cosocle | #120⋊C3 | C22×C5 |
| Frattini | C23 | C2×C5×S4 |
| Fitting | C5×H(3,𝔽4) | D3 |
| socle | C22×C5 | GL(2,ℤ/4) |
| hypocenter | C22⋊A4 | C5×D4 |
| LCS | G ▷ #120⋊C3 ▷ C22⋊A4 | |
| UCS | C1 ◁ C5 | |
246 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 246 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.
| 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)(6,7,21,10,12,20)(8,18,15)(9,14,19,17,11,13);(7,8)(9,17)(11,18)(12,16)(14,15)(19,20)80 conjugacy classes — view the full character table.
| maximal subgroup of | C5×AGL(2,ℤ/4), D5×#4625⋊C2 |
| maximal normal subgroup of | D5×#4625⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236524);