Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #453 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C83 · Schur multiplier (H2) = C23 |
| direct product | #456×C83 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C83 | #120 |
| commutator, Frattini, cosocle | C2×C4 | C23×C83 |
| prime radical | 2−1+4×C83 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C83 ◁ C2×C4×C83 ◁ G | |
142 conjugacy classes of subgroups.
1328 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C83×#1405, C83×#2203, C83×#2204, … |
| maximal normal subgroup of | C83×#1405, C83×#2203, C83×#2204, … |
| maximal quotient of | C83×#1603, C83×#1604, C83×#1605, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 137);