Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C8×Q8×C59 ⋊ C2 |
| Sylow | C59 ⋊ #2994 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D59 |
| commutator, socle | C22×C59 | C23×C4 |
| Fitting | C8×Q8×C59 | C2 |
| hypercenter | C8×Q8 | D59 |
| hypocenter | C59 | #2994 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C4 ◁ C8×Q8 | |
364 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=f,d^2=e,f^2=g,b^a=be,d^a=de,c^b=ceg,d^b=dg,h^b=h^58,h^c=h^58,h^d=h^581210 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28559840, #28559844, #28559877, … |
| maximal normal subgroup of | #28559840, #28559844, #28559877, … |
| maximal quotient of | #28587492, #28587538, #28587602, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 13669);