Finite Group DatabasebetaFinite Group Databasebeta| order | 6592 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C103 ⋊ #385 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D103 |
| commutator | C22×C103 | C22×C4 |
| Fitting | C2×C22⋊C4×C103 | C2 |
| socle | C23×C103 | C23 |
| hypercenter | C2×C22⋊C4 | D103 |
| hypocenter | C103 | #385 |
| LCS | G ▷ C22×C103 ▷ C103 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊C4 | |
234 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 91 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,b^a=bd,c^a=ce,g^a=g^102,g^b=g^1021048 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27195426, #27195427, #27196394, … |
| maximal normal subgroup of | #27195426, #27195427, #27196394, … |
| maximal quotient of | #27193366, #27193378, #27193389, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6592, 424);