Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C59 ⋊ #1312 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4×C8 | C2×D59 |
| commutator | C2×C59 | C4×C16 |
| Fitting | C4×C16×C59 | C2 |
| socle | C22×C59 | C4×C8 |
| hypercenter | C4×C16 | D59 |
| hypocenter | C59 | #1312 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C4×C8 ◁ C4×C16 | |
92 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=c,b^2=d,c^2=e,d^2=f,f^2=g,b^a=be,h^a=h^581936 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D59×#1312, C2×#21422015, #28497677, … |
| maximal normal subgroup of | D59×#1312, C2×#21422015, #28497677, … |
| maximal quotient of | #28475306, #28475516, #28476021, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 2429);