Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C83 · Schur multiplier (H2) = C25 |
| direct product | D4×Q8×C83 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C83 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C83 |
| prime radical | C2×D4×C83 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C83 ◁ G | |
280 conjugacy classes of subgroups.
2075 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C83×#1627, C83×#1637, C83×#1649, … |
| maximal normal subgroup of | C83×#1627, C83×#1637, C83×#1649, … |
| maximal quotient of | Q8×C22⋊C4×C83, D4×C4⋊C4×C83, Q8×C4⋊C4×C83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 230);