Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×#11715895 |
| derived, Sylow | C97 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | D97 |
| commutator, hypocenter | C97 | C2×C4×C8 |
| Frattini | C2×C4 | C22×D97 |
| Fitting | C2×C42×C97 | C2 |
| socle | C23×C97 | C2×C4 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C2×C42 | |
162 conjugacy classes of subgroups.
1600 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27139563, #27139570, #27139572, … |
| maximal normal subgroup of | #27139563, #27139570, #27139572, … |
| maximal quotient of | C2×C8×#11715895, C2×#20260456, M16×#11715895, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 495);