Finite Group DatabasebetaFinite Group Databasebeta| order | 6928 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C433 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | #13181884 |
| commutator, hypocenter | C433 | C16 |
| Fitting | C4×C433 | C4 |
| socle | C2×C433 | C8 |
| LCS | G ▷ C433 | |
| UCS | C1 ◁ C4 | |
10 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,433|a^2=b,b^2=c,c^2=d,e^a=e^179,e^b=e^432448 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20294100, #28357293, #28357294, … |
| maximal normal subgroup of | C2×#20294100, #28357293, #28357294, … |
| maximal quotient of | #28357270, C2×#20294100 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6928, 43);