Finite Group DatabasebetaFinite Group Databasebeta| order | 624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C3×C4×C13 ⋊ C2 |
| Hall | C3×C13 ⋊ #41 |
| Sylow | C13 ⋊ #235 |
| Sylow | C3 ⋊ #6127 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D39 |
| commutator, socle, cosocle | C2×C3×C13 | C23 |
| Frattini | C2 | C22×D39 |
| Fitting | C2×C3×C4×C13 | C2 |
| hypercenter | C2×C4 | D39 |
| hypocenter | C3×C13 | #41 |
| LCS | G ▷ C2×C3×C13 ▷ C3×C13 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 312 |
Polycyclic presentation:
2^4,3,13|b^2=d,c^a=cd,e^a=e^2,f^a=f^12162 conjugacy classes — view the full character table.
| maximal subgroup of | #11927988, #11927989, #11928117, … |
| maximal normal subgroup of | #11927988, #11927989, #11928117, … |
| maximal quotient of | C4×Dic78, #11928932, #11928934, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(624, 227);