Finite Group DatabasebetaFinite Group Databasebeta| order | 5684 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
No aliases for this group.
| Fitting, socle, derived, Hall | C72×C29 ⋊ C4 |
| Sylow | C72 ⋊ #1181 |
| Sylow | C29 ⋊ #5997 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C29 | C4 |
| LCS | G ▷ C72×C29 | |
| UCS | C1 | |
28 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,7^2,29|a^2=b,c^a=c^4d^6,d^a=c^3d^3,e^a=e^17,c^b=c^6,d^b=d^6,e^b=e^28359 conjugacy classes — view the full character table.
| maximal subgroup of | #30684952, #19150997⋊C3, C3×#19150997, … |
| maximal normal subgroup of | #19150997⋊C3, C3×#19150997, C5×#19150997 |
| maximal quotient of | C3×#19150997, C3⋊#19150997, C5×#19150997, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5684, 44);