Finite Group DatabasebetaFinite Group Databasebeta| order | 6592 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #135×C103 ⋊ C2 |
| Sylow | C103 ⋊ #578 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D4×D103 |
| commutator | C4×C103 | C24 |
| Frattini | C4 | C23×D103 |
| Fitting | #135×C103 | C2 |
| socle | C2×C103 | C22×D4 |
| hypercenter | #135 | D103 |
| hypocenter | C103 | #578 |
| LCS | G ▷ C4×C103 ▷ C2×C103 ▷ C103 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #135 | |
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,103|a^2=f,b^2=f,e^2=f,b^a=be,e^a=ef,e^b=ef,d^c=df,g^c=g^102,g^d=g^102736 conjugacy classes — view the full character table.
| maximal subgroup of | #27197105, #27197109, #27197119, … |
| maximal normal subgroup of | #27197105, #27197109, #27197119, … |
| maximal quotient of | #27203673, #27203741, #27203980, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6592, 1363);