Finite Group DatabasebetaFinite Group Databasebeta| order | 7456 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C233 ⋊ #97 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C2×D233 |
| commutator | C2×C233 | C42 |
| Fitting | C2×C8×C233 | C2 |
| socle | C22×C233 | C2×C4 |
| hypercenter | C2×C8 | D233 |
| hypocenter | C233 | #97 |
| LCS | G ▷ C2×C233 ▷ C233 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C8 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,233|a^2=c,b^2=d,c^2=e,b^a=be,f^b=f^2321876 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28416212, #97×D233, C2×#21418445, … |
| maximal normal subgroup of | #28416212, #97×D233, C2×#21418445, … |
| maximal quotient of | #28416156, #28416157, #28416189, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7456, 56);