Finite Group DatabasebetaFinite Group Databasebeta| order | 6416 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C401 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#13107944 |
| commutator, socle | C2×C401 | C2×C4 |
| Fitting | C4×C401 | C4 |
| hypercenter | C4 | #13107944 |
| hypocenter | C401 | M16 |
| LCS | G ▷ C2×C401 ▷ C401 | |
| UCS | C1 ◁ C2 ◁ C4 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,401|a^2=c,c^2=d,b^a=bd,e^a=e^20,e^b=e^400,e^c=e^400410 conjugacy classes — view the full character table.
| maximal subgroup of | #27165801, #27165802, #27165807, … |
| maximal normal subgroup of | #27165801, #27165802, #27165807, … |
| maximal quotient of | #27165792, #27165794, C4⋊#15692006, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6416, 50);