Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×Dic388 |
| Sylow | C97 ⋊ C22×Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | D388 |
| commutator | C4×C97 | C24 |
| Frattini | C4 | C23×D97 |
| Fitting | C22×C8×C97 | C2 |
| socle | C23×C97 | D4 |
| hypercenter | C22×C8 | D97 |
| hypocenter | C97 | C22×Q16 |
| LCS | G ▷ C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ C22×C8 | |
258 conjugacy classes of subgroups.
1564 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27142076, #27142078, #27142595, … |
| maximal normal subgroup of | #27142076, #27142078, #27142595, … |
| maximal quotient of | C22×#15690735, C22×#15690744, C2×C4×Dic388, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1326);