Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| isoclinism | isoclinic class of Dic94 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×C8×Dic94 |
| Sylow | C47 ⋊ C2×C8×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8 | C2×D47 |
| commutator | C2×C47 | C23×C8 |
| Frattini | C2×C4 | C23×D47 |
| Fitting | C2×C4×C8×C47 | C2 |
| socle | C23×C47 | C22×C4 |
| hypercenter | C2×C4×C8 | D47 |
| hypocenter | C47 | C2×C8×Q8 |
| LCS | G ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22×C8 ◁ C2×C4×C8 | |
440 conjugacy classes of subgroups.
1552 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#13093942, #26106852, C8×#13093949, … |
| maximal normal subgroup of | C8×#13093942, #26106852, C8×#13093949, … |
| maximal quotient of | C2×C8×C4⋊Dic47, C2×C8×Dic47⋊C4, C4×C8×Dic94, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 13431);