Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of #6728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#6729 |
| derived | SL(2,𝔽5) ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, socle, hypercenter | C2×C5 | S5 |
| commutator, cosocle, hypocenter | SL(2,𝔽5) | C2×C5 |
| Frattini | C2 | C5×S5 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2×C5 | |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 200 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | #72277246, C5×#91877, #72277297 |
| maximal normal subgroup of | #72277246, C5×#91877, #72277297 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 475);