Finite Group DatabasebetaFinite Group Databasebeta| order | 624 |
| isoclinism | isoclinic class of D39 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C23×D39 |
| Fitting, socle | C23×C3×C13 ⋊ C2 |
| derived, Hall | C3×C13 ⋊ C24 |
| Sylow | C13 ⋊ C23×D3 |
| Sylow | C3 ⋊ C23×D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D39 |
| commutator, cosocle, hypocenter | C3×C13 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C23×C3×C13 | C2 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C23 | |
268 conjugacy classes of subgroups.
| transitive degree | μt(G) = 312 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10597610, #11928697, #11928710, … |
| maximal normal subgroup of | C2×#10597610, #11928697, #11928710, … |
| maximal quotient of | C22×Dic78, C22×C4×D39, C22×D156, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(624, 259);