Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#13095490 |
| Sylow | C97 ⋊ C4×C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×D97 |
| commutator | C2×C97 | C2×C42 |
| Frattini | C23 | C22×D97 |
| Fitting | C2×C42×C97 | C2 |
| socle | C23×C97 | C23 |
| hypercenter | C2×C42 | D97 |
| hypocenter | C97 | C4×C4⋊C4 |
| LCS | G ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C42 | |
194 conjugacy classes of subgroups.
1576 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27141597, C8×#13095490, #27141602, … |
| maximal normal subgroup of | #27141597, C8×#13095490, #27141602, … |
| maximal quotient of | C4×#15690717, #27139962, #27139964, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 402);