Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×M16×C97 ⋊ C2 |
| Sylow | C97 ⋊ #575 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D388 |
| commutator | C4×C97 | C24 |
| Frattini | C4 | C23×D97 |
| Fitting | C2×M16×C97 | C2 |
| socle | C2×C97 | C22×D4 |
| hypercenter | C2×M16 | D97 |
| hypocenter | C97 | #575 |
| LCS | G ▷ C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ C2×M16 | |
262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,97|d^2=f,e^2=f,b^a=be,c^a=cf,e^a=ef,g^a=g^96,e^b=ef,g^b=g^96982 conjugacy classes — view the full character table.
| maximal subgroup of | #27142097, #27142099, #27142236, … |
| maximal normal subgroup of | #27142097, #27142099, #27142236, … |
| maximal quotient of | #27150256, #27150326, #27150538, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1349);