Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#15690732 |
| Fitting | C22×C8×C97 ⋊ C2 |
| Sylow | C97 ⋊ C2×#102 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | D388 |
| commutator | C4×C97 | C22×C4 |
| Frattini | C2×C4 | C22×D97 |
| Fitting | C22×C8×C97 | C2 |
| socle | C23×C97 | D4 |
| hypercenter | C22×C8 | D97 |
| hypocenter | C97 | C2×#102 |
| LCS | G ▷ C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ C22×C8 | |
202 conjugacy classes of subgroups.
1564 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27141550, C4×#15690732, #27141560, … |
| maximal normal subgroup of | #27141550, C4×#15690732, #27141560, … |
| maximal quotient of | C2×#20260464, #27140136, #27140162, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 537);