Finite Group DatabasebetaFinite Group Databasebeta| order | 7328 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C229 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D229 |
| commutator, socle | C2×C229 | C22×C4 |
| Fitting | #41×C229 | C2 |
| hypercenter | #41 | D229 |
| hypocenter | C229 | #131 |
| LCS | G ▷ C2×C229 ▷ C229 | |
| UCS | C1 ◁ C4 ◁ #41 | |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,229|a^2=d,d^2=e,f^a=f^228,c^b=ce1160 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28411595, #28411598, #28411600, … |
| maximal normal subgroup of | #28411595, #28411598, #28411600, … |
| maximal quotient of | #28411437, #28411448, #28411508, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7328, 153);