Finite Group DatabasebetaFinite Group Databasebeta| order | 7328 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C8×C229 ⋊ C2 |
| Sylow | C229 ⋊ #102 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D916 |
| commutator | C4×C229 | C2×C4 |
| Frattini | C2×C4 | C2×D229 |
| Fitting | C2×C8×C229 | C2 |
| socle | C22×C229 | D4 |
| hypercenter | C2×C8 | D229 |
| hypocenter | C229 | #102 |
| LCS | G ▷ C4×C229 ▷ C2×C229 ▷ C229 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×C8 | |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,229|a^2=d,c^2=e,b^a=bc,c^a=ce,f^a=f^228,c^b=ce,f^b=f^2281838 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #102×D229, C2×#20300910, #28411476, … |
| maximal normal subgroup of | #102×D229, C2×#20300910, #28411476, … |
| maximal quotient of | #28411210, #28411216, #28411224, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7328, 68);