Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C59 ⋊ #1422 |
| subgroup | G/H | |
|---|---|---|
| center | C16 | D236 |
| commutator | C4×C59 | C2×C16 |
| Frattini | C2×C16 | C2×D59 |
| Fitting | C4×C16×C59 | C2 |
| socle | C2×C59 | C4⋊C16 |
| hypercenter | C4×C16 | D59 |
| hypocenter | C59 | #1422 |
| LCS | G ▷ C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C16 ◁ C2×C16 ◁ C4×C16 | |
58 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=d,b^2=c,c^2=g,d^2=e,e^2=f,f^2=g,b^a=bc,c^a=cg,h^a=h^581912 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28476133, #28476134, #28476136, … |
| maximal normal subgroup of | #28476133, #28476134, #28476136, … |
| maximal quotient of | #28476355, #28476362, #28476380, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 2708);