Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2×C5 |
| direct product | C3×C8×C5⋊D5 |
| Fitting | C3×C52×C8 ⋊ C2 |
| derived, Sylow | C52 ⋊ C2×C3×C8 |
| Hall | C3×C52 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C8 | C5⋊D5 |
| commutator, hypocenter | C52 | C2×C3×C8 |
| Frattini | C4 | C2×C3×C5⋊D5 |
| Fitting | C3×C52×C8 | C2 |
| socle | C2×C3×C52 | C2×C4 |
| prime radical | C2×C3×C5⋊D5 | C4 |
| cosocle | C4×C52 | C22×C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C3×C8 | |
176 conjugacy classes of subgroups.
| transitive degree | μt(G) = 600 |
336 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C8×(C5⋊D5)⋊C3, C3×C8×#1043 |
| maximal normal subgroup of | C3×C8×(C5⋊D5)⋊C3, C3×C8×#1043 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 401);