Finite Group DatabasebetaFinite Group Databasebeta| order | 5008 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C313 · Schur multiplier (H2) = C22 |
| direct product | #41×C313 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C313 | C22 |
| commutator, Frattini, cosocle | C2 | C23×C313 |
| socle | C2×C313 | C23 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C313 ◁ G | |
40 conjugacy classes of subgroups.
3130 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #104×C313, #131×C313, #135×C313, … |
| maximal normal subgroup of | #104×C313, #131×C313, #135×C313, … |
| maximal quotient of | #117×C313, C4×D4×C313, C4×Q8×C313, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5008, 13);