Finite Group DatabasebetaFinite Group Databasebeta| order | 7456 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×D4×C233 ⋊ C2 |
| Sylow | C233 ⋊ H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D233 |
| commutator, socle | C2×C233 | C24 |
| Fitting | C2×D4×C233 | C2 |
| hypercenter | C2×D4 | D233 |
| hypocenter | C233 | H(5,𝔽2) |
| LCS | G ▷ C2×C233 ▷ C233 | |
| UCS | C1 ◁ C2 ◁ C2×D4 | |
166 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,233|b^a=be,d^a=de,c^b=ce,f^d=f^2321177 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28416602, #28416605, #28416612, … |
| maximal normal subgroup of | #28416602, #28416605, #28416612, … |
| maximal quotient of | #28416907, #28416908, #28416910, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7456, 191);