Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×C22⋊Dic83 |
| Sylow | C83 ⋊ C22×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C2×D83 |
| commutator | C2×C83 | C23×C4 |
| Frattini | C22 | C23×D83 |
| Fitting | C25×C83 | C2 |
| socle | C24×C83 | C22 |
| hypercenter | C25 | D83 |
| hypocenter | C83 | C22×C22⋊C4 |
| LCS | G ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C24 ◁ C25 | |
674 conjugacy classes of subgroups.
1352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#19127467, C2×#19127468, #24907535, … |
| maximal normal subgroup of | C2×#19127467, C2×#19127468, #24907535, … |
| maximal quotient of | C22×C83⋊#95, C2×C4×C22⋊Dic83, C2×#19127557, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 997);