Finite Group DatabasebetaFinite Group Databasebeta| order | 7328 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×D4×C229 ⋊ C2 |
| Sylow | C229 ⋊ H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D229 |
| commutator, socle | C2×C229 | C24 |
| Fitting | C2×D4×C229 | C2 |
| hypercenter | C2×D4 | D229 |
| hypocenter | C229 | H(5,𝔽2) |
| LCS | G ▷ C2×C229 ▷ C229 | |
| UCS | C1 ◁ C2 ◁ C2×D4 | |
166 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,229|b^a=be,d^a=de,c^b=ce,f^d=f^2281157 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28411648, #28411651, #28411658, … |
| maximal normal subgroup of | #28411648, #28411651, #28411658, … |
| maximal quotient of | #28411953, #28411954, #28411956, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7328, 191);