Finite Group DatabasebetaFinite Group Databasebeta| order | 5728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q16×C179 ⋊ C2 |
| Sylow | C179 ⋊ #135 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D179 |
| commutator | C4×C179 | C23 |
| Frattini | C4 | C22×D179 |
| Fitting | Q16×C179 | C2 |
| socle | C2×C179 | C2×D4 |
| hypercenter | Q16 | D179 |
| hypocenter | C179 | #135 |
| LCS | G ▷ C4×C179 ▷ C2×C179 ▷ C179 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q16 | |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,179|c^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^178,d^b=de,f^b=f^178,f^c=f^178637 conjugacy classes — view the full character table.
| maximal subgroup of | #26038870, #26038872, #26038876, … |
| maximal normal subgroup of | #26038870, #26038872, #26038876, … |
| maximal quotient of | #26038434, #26038476, #26038521, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5728, 169);