Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C59 ⋊ #1772 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C22⋊D59 |
| commutator | C4×C59 | C2×C42 |
| Frattini | C22×C4 | C22×D59 |
| Fitting | C59×#405 | C2 |
| socle | C22×C59 | C4×D4 |
| hypercenter | #405 | D59 |
| hypocenter | C59 | #1772 |
| LCS | G ▷ C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C8 ◁ C22×C8 ◁ #405 | |
232 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 113 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=f,c^2=de,d^2=g,b^a=bd,h^a=h^58,d^b=dg,e^b=eg1216 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28504047, #28504049, #28504052, … |
| maximal normal subgroup of | #28504047, #28504049, #28504052, … |
| maximal quotient of | #28479848, #28479852, #28479865, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 4390);