Finite Group DatabasebetaFinite Group Databasebeta| order | 8744 |
| automorphism | Aut(G) order 9548448 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D4372 |
| unambiguous semidirect product | C4⋊D1093 |
| Fitting | C4×C1093 ⋊ C2 |
| Sylow | C1093 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D1093 |
| commutator, socle | C2×C1093 | C22 |
| Fitting | C4×C1093 | C2 |
| hypercenter | C4 | D1093 |
| hypocenter | C1093 | D4 |
| LCS | G ▷ C2×C1093 ▷ C1093 | |
| UCS | C1 ◁ C2 ◁ C4 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,1093|b^a=bc,d^a=d^1092,d^b=d^10922189 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31775778, D8744, #31775780, … |
| maximal normal subgroup of | #31775778, D8744, #31775780, … |
| maximal quotient of | #31775770, C4⋊Dic1093, D8744, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8744, 10);