Finite Group DatabasebetaFinite Group Databasebeta| order | 8442 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C7×C67 ⋊ C2×C9 |
| Hall | #16862451 ⋊ C2 |
| Hall | C7×D67 ⋊ C9 |
| Hall | D67 ⋊ C7⋊C9 |
| Sylow | C67 ⋊ C2×C7⋊C9 |
| Sylow | C7 ⋊ D67⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #14584196 |
| commutator, hypocenter | C7×C67 | C2×C9 |
| Fitting, socle | C3×C7×C67 | C2×C3 |
| LCS | G ▷ C7×C67 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,67,3|b^3=e,d^a=d^66,c^b=c^2,d^b=d^29261 conjugacy classes — view the full character table.
| maximal subgroup of | #22554729⋊C2, C2×#22554729 |
| maximal normal subgroup of | #22554729⋊C2, C2×#22554729 |
| maximal quotient of | #30683047, C2×#22554729 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8442, 16);