Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×#131×C59 ⋊ C2 |
| Sylow | C59 ⋊ #3584 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×D236 |
| commutator | C4×C59 | C25 |
| Frattini | C4 | C24×D59 |
| Fitting | C2×#131×C59 | C2 |
| socle | C2×C59 | C23×D4 |
| hypercenter | C2×#131 | D59 |
| hypocenter | C59 | #3584 |
| LCS | G ▷ C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C4 ◁ C2×#41 ◁ C2×#131 | |
1424 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1424 conjugacy classes of subgroups — too many to draw. Only its 545 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,59|e^2=g,f^2=g,b^a=bf,f^a=fg,h^a=h^58,f^b=fg,h^b=h^58,d^c=dg1204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28504394, #28504397, #28504399, … |
| maximal normal subgroup of | #28504394, #28504397, #28504399, … |
| maximal quotient of | #29452255, #29452368, #29452810, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 19284);