Finite Group DatabasebetaFinite Group Databasebeta| order | 624 |
| isoclinism | isoclinic class of (C13⋊C3)⋊Q8 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×(C22⋊D13)⋊C3 |
| unambiguous semidirect product | (C2×C22⋊D13)⋊C3 |
| Fitting | C23×C13 ⋊ C2×C3 |
| Hall | C2×C22⋊D13 ⋊ C3 |
| Hall | C13⋊C3 ⋊ C2×D4 |
| Sylow | C13 ⋊ C2×C3×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D13⋊C3 |
| commutator, cosocle | C2×C13 | C23×C3 |
| Frattini | C2 | C22×D13⋊C3 |
| Fitting | C23×C13 | C2×C3 |
| socle | C22×C13 | C22×C3 |
| hypercenter | C23 | D13⋊C3 |
| hypocenter | C13 | C2×C3×D4 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ C23 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 104 |
46 conjugacy classes — view the full character table.
| maximal subgroup of | #88046⋊C3, #88119⋊C3, #88121⋊C3, … |
| maximal normal subgroup of | #88046⋊C3, #88119⋊C3, #88121⋊C3, … |
| maximal quotient of | C2×#6101⋊C3, #88178⋊C3, C2×#6103⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(624, 146);