Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of #10597167 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×#10597167 |
| Fitting, socle | C2×C52 ⋊ C3⋊C8 |
| derived, Hall | C52⋊C3 ⋊ C2×C8 |
| Sylow | C52 ⋊ C2×C3⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #10597167 |
| commutator, hypocenter | C52⋊C3 | C2×C8 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52 | C3⋊C8 |
| prime radical | C2×(C5⋊D5)⋊C3 | C4 |
| cosocle | #1043⋊C3 | C22 |
| LCS | G ▷ C52⋊C3 | |
| UCS | C1 ◁ C2 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 50 |
26 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72210663, C2×AΓL(1,𝔽25), C22×#10597167, … |
| maximal normal subgroup of | C2×AΓL(1,𝔽25), C22×#10597167, C4×#10597167, … |
| maximal quotient of | C22×#10597167, D3×#10597167, C4×#10597167 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 948);