Finite Group DatabasebetaFinite Group Databasebeta| order | 5672 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C709 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #15667778 |
| commutator, hypocenter | C709 | C8 |
| Fitting, socle | C2×C709 | C4 |
| LCS | G ▷ C709 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,709|a^2=b,b^2=c,d^a=d^96,d^b=d^708362 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#19150893, D709⋊C8, #26015402, … |
| maximal normal subgroup of | C2×#19150893, D709⋊C8, #26015402, … |
| maximal quotient of | #26015396, C2×#19150893 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5672, 13);