Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#15689598 |
| Sylow | C47 ⋊ C2×#518 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D47 |
| commutator | C2×C47 | C24×C4 |
| Frattini | C22 | C24×D47 |
| Fitting | C23×D4×C47 | C2 |
| socle | C23×C47 | C24 |
| hypercenter | C23×D4 | D47 |
| hypocenter | C47 | C2×#518 |
| LCS | G ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ C23×D4 | |
1920 conjugacy classes of subgroups; only the 1077 normal subgroups are shown.
This group has 1920 conjugacy classes of subgroups — too many to draw. Only its 1077 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
988 conjugacy classes — view the full character table.
| maximal subgroup of | #26121595, #26121598, #26121620, … |
| maximal normal subgroup of | #26121595, #26121598, #26121620, … |
| maximal quotient of | C2×#20245741, C2×#20245745, C2×#20245749, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 17697);