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 ⋊ #538 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D97 |
| commutator, socle | C22×C97 | C24 |
| Fitting | C22⋊Q8×C97 | C2 |
| hypercenter | C22⋊Q8 | D97 |
| hypocenter | C97 | #538 |
| LCS | G ▷ C22×C97 ▷ C97 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
250 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,97|b^2=f,b^a=be,c^a=cf,d^a=de,g^a=g^96,c^b=ce,g^b=g^96,g^c=g^96694 conjugacy classes — view the full character table.
| maximal subgroup of | #27140681, #27140685, #27140715, … |
| maximal normal subgroup of | #27140681, #27140685, #27140715, … |
| maximal quotient of | #27144333, #27144364, #27144393, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1139);