Finite Group DatabasebetaFinite Group Databasebeta| order | 6544 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C409 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×D409 |
| commutator, socle | C2×C409 | C2×C4 |
| Fitting | C2×C4×C409 | C2 |
| hypercenter | C2×C4 | D409 |
| hypocenter | C409 | M16 |
| LCS | G ▷ C2×C409 ▷ C409 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,409|a^2=c,c^2=d,b^a=bd,e^a=e^4081642 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27189633, #27189634, #27189635, … |
| maximal normal subgroup of | #27189633, #27189634, #27189635, … |
| maximal quotient of | #27189628, C22⋊#15692543, C4⋊#15692543, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6544, 24);