Finite Group DatabasebetaFinite Group Databasebeta| order | 7328 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C229 ⋊ #97 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C2×D229 |
| commutator | C2×C229 | C42 |
| Fitting | C42×C229 | C2 |
| socle | C22×C229 | C2×C4 |
| hypercenter | C42 | D229 |
| hypocenter | C229 | #97 |
| LCS | G ▷ C2×C229 ▷ C229 | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,229|a^2=c,b^2=d,c^2=e,b^a=be,f^a=f^2281844 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28411220, #28411221, #28411222, … |
| maximal normal subgroup of | #28411220, #28411221, #28411222, … |
| maximal quotient of | #28411203, #28411236, #28411259, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7328, 57);