Finite Group DatabasebetaFinite Group Databasebeta| order | 624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C22 |
| direct product | D3×Q8×C13 |
| Fitting | C3×Q8×C13 ⋊ C2 |
| Hall | C3×C13 ⋊ C2×Q8 |
| Sylow | C3 ⋊ C2×Q8×C13 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 312 |
195 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#6106, D3×#6107, #11928659, … |
| maximal normal subgroup of | D3×#6106, D3×#6107, #11928659, … |
| maximal quotient of | C13×#887, C13×#896, C13×#888, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(624, 220);