Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#15690769 |
| Sylow | C97 ⋊ C2×#117 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×D97 |
| commutator | C2×C97 | C23×C4 |
| Frattini | C22 | C23×D97 |
| Fitting | C23×C4×C97 | C2 |
| socle | C23×C97 | C23 |
| hypercenter | C23×C4 | D97 |
| hypocenter | C97 | C2×#117 |
| LCS | G ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C22×C4 ◁ C23×C4 | |
330 conjugacy classes of subgroups.
1576 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27141432, #27141434, C2×#20260491, … |
| maximal normal subgroup of | #27141432, #27141434, C2×#20260491, … |
| maximal quotient of | C2×#20260581, C2×C4×C22⋊Dic97, C2×C4×C4⋊Dic97, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1005);