Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#14581716 |
| Sylow | C83 ⋊ C2×#103 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22⋊D83 |
| commutator | C4×C83 | C22×C4 |
| Frattini | C2×C4 | C22×D83 |
| Fitting | C22×Q8×C83 | C2 |
| socle | C23×C83 | D4 |
| hypercenter | C22×Q8 | D83 |
| hypocenter | C83 | C2×#103 |
| LCS | G ▷ C4×C83 ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ C22×Q8 | |
162 conjugacy classes of subgroups.
848 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#14581716, #103×Dic83, #24907293, … |
| maximal normal subgroup of | C4×#14581716, #103×Dic83, #24907293, … |
| maximal quotient of | C2×#19127463, C4×#14581716, #24907398, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 540);