Finite Group DatabasebetaFinite Group Databasebeta| order | 10718 |
| isoclinism | isoclinic class of D233 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×D233 |
| unambiguous semidirect product | C233⋊(C2×C23) |
| Fitting, socle, Hall | C23×C233 ⋊ C2 |
| derived, Sylow | C233 ⋊ C2×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D233 |
| commutator, cosocle, hypocenter | C233 | C2×C23 |
| Frattini | C1 | G |
| Fitting, socle | C23×C233 | C2 |
| LCS | G ▷ C233 | |
| UCS | C1 ◁ C23 | |
8 conjugacy classes of subgroups.
2714 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×#11745400, C23⋊#11745400, D23×D233, … |
| maximal normal subgroup of | C23×#11745400, C23⋊#11745400, D23×D233, … |
| maximal quotient of | C23×Dic233, C2×C23×D233, C3×C23×D233, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10718, 2);