Finite Group DatabasebetaFinite Group Databasebeta| order | 6700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C67⋊#1044 |
| Fitting, socle, derived, Hall | C52×C67 ⋊ C4 |
| Sylow | C67 ⋊ #1044 |
| Sylow | C52 ⋊ Dic67 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C67 | C4 |
| LCS | G ▷ C52×C67 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5^2,67|a^2=b,c^a=c^2,d^a=d^3,e^a=e^66,c^b=c^4,d^b=d^4472 conjugacy classes — view the full character table.
| maximal subgroup of | C67⋊#64480, (C67⋊C3)⋊#1044, C3×C67⋊#1044, … |
| maximal normal subgroup of | (C67⋊C3)⋊#1044, C3×C67⋊#1044 |
| maximal quotient of | C3×C67⋊#1044, C3⋊(C67⋊#1044) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6700, 25);