Finite Group DatabasebetaFinite Group Databasebeta| order | 624 |
| isoclinism | isoclinic class of C13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C16 · Schur multiplier (H2) = C1 |
| direct product | C16×C13⋊C3 |
| unambiguous semidirect product | (C13×C16)⋊C3 |
| Fitting, Hall | C13×C16 ⋊ C3 |
| derived, Sylow | C13 ⋊ C3×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | C13⋊C3 |
| commutator, hypocenter | C13 | C3×C16 |
| Frattini | C8 | C2×C13⋊C3 |
| Fitting | C13×C16 | C3 |
| socle | C2×C13 | C3×C8 |
| prime radical | C2×C13⋊C3 | C8 |
| cosocle | C8×C13 | C2×C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C16 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #88034⋊C3, C32×C13⋊C3, C16×D13⋊C3, … |
| maximal normal subgroup of | #88034⋊C3, C32×C13⋊C3, C16×D13⋊C3, … |
| maximal quotient of | C32×C13⋊C3, C2×C16×C13⋊C3, C16×C13⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(624, 2);