Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C22×#13050574 |
| Sylow | C83 ⋊ C22×M16 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×D83 |
| commutator | C2×C83 | C23×C4 |
| Frattini | C4 | C23×D83 |
| Fitting | C23×C4×C83 | C2 |
| socle | C23×C83 | C2×C4 |
| hypercenter | C23×C4 | D83 |
| hypocenter | C83 | C22×M16 |
| LCS | G ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C22×C4 ◁ C23×C4 | |
298 conjugacy classes of subgroups.
1352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #24907156, #24907157, #24907159, … |
| maximal normal subgroup of | #24907156, #24907157, #24907159, … |
| maximal quotient of | C22×#14581703, C2×C4×#13050574, C22×C22⋊(C83⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 1309);