Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | C2×#14581731 |
| Fitting | C2×C16×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×M32 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C2×D83 |
| commutator | C2×C83 | C22×C8 |
| Frattini | C8 | C22×D83 |
| Fitting | C2×C16×C83 | C2 |
| socle | C22×C83 | C2×C8 |
| hypercenter | C2×C16 | D83 |
| hypocenter | C83 | C2×M32 |
| LCS | G ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C2×C8 ◁ C2×C16 | |
90 conjugacy classes of subgroups.
1352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#14581731, #24909056, #24909058, … |
| maximal normal subgroup of | C4×#14581731, #24909056, #24909058, … |
| maximal quotient of | C2×#19127476, C4×#14581731, C2×(C2×D83)⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 963);