Finite Group DatabasebetaFinite Group Databasebeta| order | 8264 |
| automorphism | Aut(G) order 8528448 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D4132 |
| unambiguous semidirect product | C4⋊D1033 |
| Fitting | C4×C1033 ⋊ C2 |
| Sylow | C1033 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D1033 |
| commutator, socle | C2×C1033 | C22 |
| Fitting | C4×C1033 | C2 |
| hypercenter | C4 | D1033 |
| hypocenter | C1033 | D4 |
| LCS | G ▷ C2×C1033 ▷ C1033 | |
| UCS | C1 ◁ C2 ◁ C4 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,1033|b^a=bc,d^a=d^1032,d^b=d^10322069 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30658310, D8264, #30658312, … |
| maximal normal subgroup of | #30658310, D8264, #30658312, … |
| maximal quotient of | #30658302, C4⋊Dic1033, D8264, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8264, 10);