Finite Group DatabasebetaFinite Group Databasebeta| order | 624 |
| isoclinism | isoclinic class of #64602 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#64604 |
| Hall | C3×C13 ⋊ C2×D4 |
| Sylow | C13 ⋊ C2×D12 |
| Sylow | C3 ⋊ C2×C22⋊D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×D13 |
| commutator, cosocle | C2×C3×C13 | C23 |
| Frattini | C2 | C2×D3×D13 |
| Fitting, socle | C22×C3×C13 | C22 |
| hypocenter | C3×C13 | C2×D4 |
| LCS | G ▷ C2×C3×C13 ▷ C3×C13 | |
| UCS | C1 ◁ C22 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 312 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | #11928221, #11928534, #11928538, … |
| maximal normal subgroup of | #11928221, #11928534, #11928538, … |
| maximal quotient of | #11928452, #11928454, #11928460, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(624, 189);