Finite Group DatabasebetaFinite Group Databasebeta| order | 624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×Q8×D13 |
| Fitting | C3×Q8×C13 ⋊ C2 |
| Hall | C3×C13 ⋊ C2×Q8 |
| Sylow | C13 ⋊ C2×C3×Q8 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 312 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#88117, #11928380, D13×#215, … |
| maximal normal subgroup of | C3×#88117, #11928380, D13×#215, … |
| maximal quotient of | C3×#88141, C3×#88150, C3×#88142, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(624, 210);