Finite Group DatabasebetaFinite Group Databasebeta| order | 5728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C179 ⋊ #125 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D179 |
| commutator, socle | C22×C179 | C23 |
| Fitting | C4⋊C4×C179 | C2 |
| hypercenter | C4⋊C4 | D179 |
| hypocenter | C179 | #125 |
| LCS | G ▷ C22×C179 ▷ C179 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,179|a^2=d,b^2=e,c^2=d,b^a=bd,c^a=ce,f^b=f^178,f^c=f^178904 conjugacy classes — view the full character table.
| maximal subgroup of | #26038737, #26038738, #26038741, … |
| maximal normal subgroup of | #26038737, #26038738, #26038741, … |
| maximal quotient of | #26038304, #26038322, #26038326, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5728, 137);