Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22⋊Q8×C97 ⋊ C2 |
| Sylow | C97 ⋊ #552 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D97 |
| commutator, socle | C22×C97 | C24 |
| Fitting | C22⋊Q8×C97 | C2 |
| hypercenter | C22⋊Q8 | D97 |
| hypocenter | C97 | #552 |
| LCS | G ▷ C22×C97 ▷ C97 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
214 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 214 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:
2^6,97|a^2=e,b^2=f,c^2=e,b^a=be,c^a=cf,g^a=g^96,d^b=de,g^b=g^96,g^c=g^96697 conjugacy classes — view the full character table.
| maximal subgroup of | #27153575, #27153577, #27153627, … |
| maximal normal subgroup of | #27153575, #27153577, #27153627, … |
| maximal quotient of | #27144594, #27144607, #27144620, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1241);