Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | #117×C97 ⋊ C2 |
| Sylow | C97 ⋊ #410 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #13095488 |
| commutator | C22×C97 | C22×C4 |
| Frattini | C23 | C22×D97 |
| Fitting | #117×C97 | C2 |
| socle | C2×C97 | C2×C22⋊C4 |
| hypercenter | #117 | D97 |
| hypocenter | C97 | #410 |
| LCS | G ▷ C22×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #117 | |
158 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 59 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,c^2=f,b^a=bd,d^a=df,e^b=ef,g^b=g^96982 conjugacy classes — view the full character table.
| maximal subgroup of | #27141535, #27141537, #27141698, … |
| maximal normal subgroup of | #27141535, #27141537, #27141698, … |
| maximal quotient of | #27140048, #27140056, #27140059, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 522);