Finite Group DatabasebetaFinite Group Databasebeta| order | 6700 |
| isoclinism | isoclinic class of #1042 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C67 · Schur multiplier (H2) = C1 |
| direct product | C67×#1042 |
| Fitting, socle, Hall | C52×C67 ⋊ C4 |
| derived, Sylow | C52 ⋊ C4×C67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C67 | #1042 |
| commutator, hypocenter | C52 | C4×C67 |
| Frattini | C1 | G |
| Fitting, socle | C52×C67 | C4 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C67 | |
26 conjugacy classes of subgroups.
871 conjugacy classes — view the full character table.
| maximal subgroup of | #1042×C67⋊C3, C3×C67×#1042, C67×C3⋊#1042 |
| maximal normal subgroup of | #1042×C67⋊C3, C3×C67×#1042 |
| maximal quotient of | C3×C67×#1042, C67×C3⋊#1042 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6700, 26);