Finite Group DatabasebetaFinite Group Databasebeta| order | 5728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #41×C179 ⋊ C2 |
| Sylow | C179 ⋊ H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D179 |
| commutator, socle | C2×C179 | C24 |
| Fitting | #41×C179 | C2 |
| hypercenter | #41 | D179 |
| hypocenter | C179 | H(5,𝔽2) |
| LCS | G ▷ C2×C179 ▷ C179 | |
| UCS | C1 ◁ C2 ◁ #41 | |
166 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,179|b^a=be,d^a=de,c^b=ce,f^c=f^178,f^d=f^178907 conjugacy classes — view the full character table.
| maximal subgroup of | #26038605, #26038608, #26038615, … |
| maximal normal subgroup of | #26038605, #26038608, #26038615, … |
| maximal quotient of | #26038911, #26038913, #26038919, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5728, 192);