Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C59 ⋊ #2848 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D59 |
| commutator, socle | C23×C59 | C24 |
| Fitting | C24×C4×C59 | C2 |
| hypercenter | C24×C4 | D59 |
| hypocenter | C59 | #2848 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C24×C4 | |
1068 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 237 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,59|a^2=e,b^2=e,b^a=be,c^a=cf,d^a=dg,h^a=h^581900 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28484242, #28484244, #28484262, … |
| maximal normal subgroup of | #28484242, #28484244, #28484262, … |
| maximal quotient of | #28519849, #28519898, #28519911, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 12797);