Finite Group DatabasebetaFinite Group Databasebeta| order | 10348 |
| automorphism | Aut(G) order 12293424 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D5174 |
| direct product | C2×D2587 |
| unambiguous semidirect product | (C2×C13)⋊D199 |
| unambiguous semidirect product | (C2×C199)⋊D13 |
| Fitting, socle | C2×C13×C199 ⋊ C2 |
| derived, Hall | C13×C199 ⋊ C22 |
| Sylow | C199 ⋊ C2×D13 |
| Sylow | C13 ⋊ C2×D199 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2587 |
| commutator, cosocle, hypocenter | C13×C199 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C13×C199 | C2 |
| LCS | G ▷ C13×C199 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
2590 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#29509401, C2×#29509400, C2×(C13⋊C3)⋊D199, … |
| maximal normal subgroup of | C2×#29509401, C2×#29509400, C2×(C13⋊C3)⋊D199, … |
| maximal quotient of | D3×D2587, C2×C3×D2587, C2×D7761, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10348, 9);