Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×C83⋊C8 |
| derived, Sylow | C83 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | D83 |
| commutator, hypocenter | C83 | C2×C4×C8 |
| Frattini | C2×C4 | C22×D83 |
| Fitting | C2×C42×C83 | C2 |
| socle | C23×C83 | C2×C4 |
| LCS | G ▷ C83 | |
| UCS | C1 ◁ C2×C42 | |
162 conjugacy classes of subgroups.
1376 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C8×Dic83, C42×C83⋊C8, C4×#14581702, … |
| maximal normal subgroup of | C4×C8×Dic83, C42×C83⋊C8, C4×#14581702, … |
| maximal quotient of | C42×C83⋊C8, C2×#19127456, #24907209, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 495);