Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C23×C83⋊C8 |
| derived, Sylow | C83 ⋊ C23×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | D83 |
| commutator, hypocenter | C83 | C23×C8 |
| Frattini | C4 | C23×D83 |
| Fitting | C23×C4×C83 | C2 |
| socle | C24×C83 | C4 |
| LCS | G ▷ C83 | |
| UCS | C1 ◁ C23×C4 | |
338 conjugacy classes of subgroups.
1376 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#19127455, C2×#19127456, #24907160, … |
| maximal normal subgroup of | C2×#19127455, C2×#19127456, #24907160, … |
| maximal quotient of | C22×C4×C83⋊C8, C22×C22⋊(C83⋊C8), C22×C4⋊(C83⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 1306);