Finite Group DatabasebetaFinite Group Databasebeta| order | 10350 |
| isoclinism | isoclinic class of C52⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C23 · Schur multiplier (H2) = C3×C5 |
| Fitting, socle | C2×C3×C52×C23 ⋊ C3 |
| derived, Sylow | C52 ⋊ C2×C32×C23 |
| Hall | C2×C52×C23 ⋊ C32 |
| Hall | C52×C23 ⋊ C2×C32 |
| Hall | C2×C52 ⋊ C32×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C23 | C52⋊C3 |
| commutator, cosocle, hypocenter | C52 | C2×C32×C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C52×C23 | C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C3×C23 | |
64 conjugacy classes of subgroups.
1518 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C23×#64470, C3×C23⋊#64470, C3×C23×#1039⋊C3, … |
| maximal normal subgroup of | C3×C23×#64470, C3×C23⋊#64470, C3×C23×#1039⋊C3, … |
| maximal quotient of | C3×C4×C23×C52⋊C3, C22×C3×C23×C52⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10350, 51);