Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#15690897 |
| Sylow | C97 ⋊ C2×#131 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×#87604 |
| commutator | C2×C97 | C23×C4 |
| Frattini | C2 | C23×#87604 |
| Fitting | C2×D4×C97 | C4 |
| socle | C22×C97 | C22×C4 |
| hypercenter | C2×D4 | #87604 |
| hypocenter | C97 | C2×#131 |
| LCS | G ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
266 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 140 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
280 conjugacy classes — view the full character table.
| maximal subgroup of | #27157493, #27157494, #27157511, … |
| maximal normal subgroup of | #27157493, #27157494, #27157511, … |
| maximal quotient of | C2×#20261699, C2×#20261700, C4×#15690897, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1624);