Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C59 ⋊ C2 |
| Sylow | C59 ⋊ #2352 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D59 |
| commutator | C22×C59 | C23×C4 |
| Fitting | C4×C4⋊C4×C59 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | C4×C4⋊C4 | D59 |
| hypocenter | C59 | #2352 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C4×C4⋊C4 | |
660 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=g,b^2=f,c^2=f,b^a=be,c^a=cf,h^a=h^58,d^b=de,h^b=h^58,h^d=h^581210 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28604111, #28604113, #28604137, … |
| maximal normal subgroup of | #28604111, #28604113, #28604137, … |
| maximal quotient of | C4⋊C4×(C2×D59)⋊C4, #28510110, #28510135, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 7442);