Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C59 ⋊ C2 |
| Sylow | C59 ⋊ #2597 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D59 |
| commutator, socle | C23×C59 | C24 |
| Fitting | C4×C4⋊C4×C59 | C2 |
| hypercenter | C4×C4⋊C4 | D59 |
| hypocenter | C59 | #2597 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C4×C4⋊C4 | |
454 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=eg,b^2=fg,c^2=g,d^2=ef,b^a=be,c^a=cf,d^a=de,h^a=h^58,c^b=cg1198 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D59×#2597, C2×#21429647, #28759289, … |
| maximal normal subgroup of | D59×#2597, C2×#21429647, #28759289, … |
| maximal quotient of | #28511184, #28511295, #28512304, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 10061);