Finite Group DatabasebetaFinite Group Databasebeta| order | 5728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C179 ⋊ C2 |
| Sylow | C179 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D179 |
| commutator, socle | C2×C179 | C22×C4 |
| Fitting | M16×C179 | C2 |
| hypercenter | M16 | D179 |
| hypocenter | C179 | #131 |
| LCS | G ▷ C2×C179 ▷ C179 | |
| UCS | C1 ◁ C4 ◁ M16 | |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,179|a^2=d,d^2=e,f^a=f^178,c^b=ce,f^c=f^178910 conjugacy classes — view the full character table.
| maximal subgroup of | #26038553, #26038555, #26038558, … |
| maximal normal subgroup of | #26038553, #26038555, #26038558, … |
| maximal quotient of | #26038396, #26038397, #26038404, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5728, 154);