Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C59×#322 ⋊ C2 |
| Sylow | C59 ⋊ #1719 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #14273724 |
| commutator | C42×C59 | C23 |
| Frattini | C42 | C22×D59 |
| Fitting | C59×#322 | C2 |
| socle | C22×C59 | #127 |
| hypercenter | #322 | D59 |
| hypocenter | C59 | #1719 |
| LCS | G ▷ C42×C59 ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #322 | |
186 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,59|b^2=dfg,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^58,c^b=cf1186 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D59×#1719, C2×#21423749, #28576459, … |
| maximal normal subgroup of | D59×#1719, C2×#21423749, #28576459, … |
| maximal quotient of | #28482484, #28488461, #28488482, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 4163);