Finite Group DatabasebetaFinite Group Databasebeta| order | 8468 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C29×C73 ⋊ C4 |
| Sylow | C73 ⋊ #1181 |
| Sylow | C29 ⋊ Dic73 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C29×C73 | C4 |
| LCS | G ▷ C29×C73 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,29,73|a^2=b,c^a=c^17,d^a=d^72,c^b=c^28587 conjugacy classes — view the full character table.
| maximal subgroup of | #22554977⋊C3, C3×#22554977, C3⋊#22554977 |
| maximal normal subgroup of | #22554977⋊C3, C3×#22554977 |
| maximal quotient of | C3×#22554977, C3⋊#22554977 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8468, 10);