Finite Group DatabasebetaFinite Group Databasebeta| order | 10350 |
| isoclinism | isoclinic class of C3⋊(C3⋊(C5⋊D5)) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C3×C5 |
| direct product | C23×C3⋊(C3⋊(C5⋊D5)) |
| unambiguous semidirect product | C3⋊(C23×C3⋊(C5⋊D5)) |
| unambiguous semidirect product | C5⋊(C23×C3⋊D15) |
| Fitting, socle, Hall | C32×C52×C23 ⋊ C2 |
| derived, Hall | C32×C52 ⋊ C2×C23 |
| Hall | C52×C23 ⋊ C3⋊D3 |
| Hall | C32×C23 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ C3⋊D3×C23 |
| Sylow | C32 ⋊ C23×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C3⋊(C3⋊(C5⋊D5)) |
| commutator, cosocle, hypocenter | C32×C52 | C2×C23 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C23 | C2 |
| LCS | G ▷ C32×C52 | |
| UCS | C1 ◁ C23 | |
192 conjugacy classes of subgroups.
2622 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×#11744707, C23⋊#11744707, C23×#11744708, … |
| maximal normal subgroup of | C23×#11744707, C23⋊#11744707, C23×#11744708, … |
| maximal quotient of | C23×C3⋊(C3⋊#1039), C2×C23×C3⋊(C3⋊(C5⋊D5)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10350, 53);