Finite Group DatabasebetaFinite Group Databasebeta| order | 624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C13 ⋊ Q16 |
| Sylow | C13 ⋊ #216 |
| Sylow | C3 ⋊ #6107 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #64602 |
| commutator, Fitting, cosocle | C3×C4×C13 | C22 |
| Frattini, hypercenter | C4 | D3×D13 |
| socle, prime radical | C2×C3×C13 | D4 |
| hypocenter | C3×C13 | Q16 |
| LCS | G ▷ C3×C4×C13 ▷ C2×C3×C13 ▷ C3×C13 | |
| UCS | C1 ◁ C2 ◁ C4 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 624 |
Polycyclic presentation:
2^4,3,13|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,f^a=f^12,c^b=cd,e^b=e^266 conjugacy classes — view the full character table.
| maximal subgroup of | #11928405, #11928417, #11928418, … |
| maximal normal subgroup of | #11928405, #11928417, #11928418, … |
| maximal quotient of | #11927978, #11927980, #11927997, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(624, 41);