Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C23×Dic194 |
| Sylow | C97 ⋊ C23×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C2×D97 |
| commutator | C2×C97 | C25 |
| Frattini | C2 | C24×D97 |
| Fitting | C23×C4×C97 | C2 |
| socle | C24×C97 | C22 |
| hypercenter | C23×C4 | D97 |
| hypocenter | C97 | C23×Q8 |
| LCS | G ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C24 ◁ C23×C4 | |
850 conjugacy classes of subgroups.
1576 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27140006, #27141659, #27141670, … |
| maximal normal subgroup of | #27140006, #27141659, #27141670, … |
| maximal quotient of | C23×#13095490, C23×C4⋊Dic97, C22×C4×Dic194, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1373);