Finite Group DatabasebetaFinite Group Databasebeta| order | 7456 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C8×C233 ⋊ C2 |
| Sylow | C233 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | C2×D233 |
| commutator, socle | C2×C233 | C22×C4 |
| Frattini | C4 | C22×D233 |
| Fitting | C2×C8×C233 | C2 |
| hypercenter | C2×C8 | D233 |
| hypocenter | C233 | #131 |
| LCS | G ▷ C2×C233 ▷ C233 | |
| UCS | C1 ◁ C8 ◁ C2×C8 | |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,233|a^2=d,d^2=e,c^b=ce,f^c=f^2321876 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28416218, #28416220, #28416550, … |
| maximal normal subgroup of | #28416218, #28416220, #28416550, … |
| maximal quotient of | #28416389, #28416390, #28416400, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7456, 152);