Finite Group DatabasebetaFinite Group Databasebeta| order | 31164 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, Hall | C72×C53 ⋊ Dic3 |
| derived, Hall | C53×#3862 ⋊ C4 |
| Hall | #3862 ⋊ #6157 |
| Sylow | C53 ⋊ #10596868 |
| Sylow | C72 ⋊ C3⋊#6157 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C53×#3862 | C4 |
| Fitting, socle | C72×C53 | Dic3 |
| prime radical, cosocle | D53×#3862 | C2 |
| LCS | G ▷ C53×#3862 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 742 |
Polycyclic presentation:
2^2,3,53,7^2|a^2=b,c^a=c^2,d^a=d^30,e^a=e^4f,f^a=e^6f^3,d^b=d^52,e^c=e^2f^6,f^c=f^4287 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31164, 76);