Finite Group DatabasebetaFinite Group Databasebeta| order | 7328 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×Q8×C229 ⋊ C2 |
| Sylow | C229 ⋊ 2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D229 |
| commutator, socle | C2×C229 | C24 |
| Fitting | C2×Q8×C229 | C2 |
| hypercenter | C2×Q8 | D229 |
| hypocenter | C229 | 2−1+4 |
| LCS | G ▷ C2×C229 ▷ C229 | |
| UCS | C1 ◁ C2 ◁ C2×Q8 | |
146 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,229|b^2=e,c^2=e,b^a=be,d^a=de,c^b=ce,f^b=f^228,f^d=f^2281157 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28411653, #28411656, #28411663, … |
| maximal normal subgroup of | #28411653, #28411656, #28411663, … |
| maximal quotient of | #28411957, #28411959, #28411962, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7328, 194);