Finite Group DatabasebetaFinite Group Databasebeta| order | 624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | Q8×D39 |
| Fitting | C3×Q8×C13 ⋊ C2 |
| Hall | C3×C13 ⋊ C2×Q8 |
| Sylow | C13 ⋊ D3×Q8 |
| Sylow | C3 ⋊ Q8×D13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D39 |
| commutator, socle, cosocle | C2×C3×C13 | C23 |
| Fitting | C3×Q8×C13 | C2 |
| prime radical | C2×D39 | C22 |
| hypercenter | Q8 | D39 |
| hypocenter | C3×C13 | C2×Q8 |
| LCS | G ▷ C2×C3×C13 ▷ C3×C13 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 312 |
105 conjugacy classes — view the full character table.
| maximal subgroup of | #11928646, #11928652, #11928663, … |
| maximal normal subgroup of | #11928646, #11928652, #11928663, … |
| maximal quotient of | #11928949, #11928950, #11928951, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(624, 230);