Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×D8×C97 ⋊ C2 |
| Sylow | C97 ⋊ #459 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D4×D97 |
| commutator | C2×C4×C97 | C23 |
| Frattini | C2×C4 | C22×D97 |
| Fitting | C2×D8×C97 | C2 |
| socle | C22×C97 | C2×D4 |
| hypercenter | C2×D8 | D97 |
| hypocenter | C97 | #459 |
| LCS | G ▷ C2×C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×D8 | |
140 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 43 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=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^b=g^96,e^c=ef691 conjugacy classes — view the full character table.
| maximal subgroup of | #459×D97, C2×#20260928, #27151187, … |
| maximal normal subgroup of | #459×D97, C2×#20260928, #27151187, … |
| maximal quotient of | #27141075, #27141079, #27141089, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 742);