Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C59×#568 ⋊ C2 |
| Sylow | C59 ⋊ #3573 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C24×D59 |
| commutator, socle | C2×C59 | C24×C4 |
| Fitting | C59×#568 | C2 |
| hypercenter | #568 | D59 |
| hypocenter | C59 | #3573 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C4 ◁ #568 | |
1424 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=f,f^2=g,h^a=h^58,e^b=eg,d^c=dg,h^e=h^581054 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28594648, #28594650, #28594654, … |
| maximal normal subgroup of | #28594648, #28594650, #28594654, … |
| maximal quotient of | #29452111, #29452112, #29452113, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 19223);