Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | C2×#15690722 |
| Fitting | C22×C8×C97 ⋊ C2 |
| Sylow | C97 ⋊ C2×C22⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×D97 |
| commutator | C2×C97 | C22×C8 |
| Frattini | C2×C4 | C22×D97 |
| Fitting | C22×C8×C97 | C2 |
| socle | C23×C97 | C2×C4 |
| hypercenter | C22×C8 | D97 |
| hypocenter | C97 | C2×C22⋊C8 |
| LCS | G ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C8 | |
202 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1576 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27139659, #27141493, C4×#15690722, … |
| maximal normal subgroup of | #27139659, #27141493, C4×#15690722, … |
| maximal quotient of | C2×#20260458, C2×#20260460, #27140048, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 509);