Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C59×#433 ⋊ C2 |
| Sylow | C59 ⋊ #2978 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D59 |
| commutator, socle | C22×C59 | C23×C4 |
| Fitting | C59×#433 | C2 |
| hypercenter | #433 | D59 |
| hypocenter | C59 | #2978 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C4 ◁ #433 | |
402 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 157 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=f,f^2=g,b^a=be,c^a=cg,d^a=de,c^b=ceg,d^b=dg,h^b=h^58,h^c=h^58850 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#2978, C2×#21433157, #29453485, … |
| maximal normal subgroup of | D59×#2978, C2×#21433157, #29453485, … |
| maximal quotient of | #28587393, #28587414, #28587471, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 13571);