Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×#13050580 |
| Sylow | C83 ⋊ C22×Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22⋊D83 |
| commutator | C4×C83 | C24 |
| Frattini | C4 | C23×D83 |
| Fitting | C22×Q8×C83 | C2 |
| socle | C23×C83 | D4 |
| hypercenter | C22×Q8 | D83 |
| hypocenter | C83 | C22×Q16 |
| LCS | G ▷ C4×C83 ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ C22×Q8 | |
258 conjugacy classes of subgroups.
848 conjugacy classes — view the full character table.
| maximal subgroup of | #24907801, #24907802, #24907804, … |
| maximal normal subgroup of | #24907801, #24907802, #24907804, … |
| maximal quotient of | C22×#14581715, C22×#14581716, C22×#14581725, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 1325);