Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C83 · Schur multiplier (H2) = C22 |
| direct product | C2×#108×C83 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C83 | D4 |
| commutator | C4 | C22×C4×C83 |
| Frattini, cosocle | C2×C4 | C23×C83 |
| socle | C22×C83 | C4⋊C4 |
| prime radical | C23×C83 | Q8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C83 ◁ C22×C4×C83 ◁ G | |
106 conjugacy classes of subgroups.
2324 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C83×#1381, C83×#1382, C83×#1383, … |
| maximal normal subgroup of | C83×#1381, C83×#1382, C83×#1383, … |
| maximal quotient of | C2×#334×C83, C2×#335×C83, C83×#1564, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 110);