Finite Group DatabasebetaFinite Group Databasebeta| order | 31164 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C53×#3862 ⋊ C4 |
| Hall | C72×C53 ⋊ Dic3 |
| Hall | #3862 ⋊ Dic53 |
| Sylow | C53 ⋊ #10596868 |
| Sylow | C72 ⋊ Dic159 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C53⋊#64418 |
| commutator, hypocenter | C53×#3862 | C4 |
| Fitting, socle | C2×C72×C53 | D3 |
| prime radical, cosocle | C2×C53×#3862 | C2 |
| LCS | G ▷ C53×#3862 | |
| UCS | C1 ◁ C2 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1484 |
Polycyclic presentation:
2,3,53,7^2,2|a^2=f,b^a=b^2,c^a=c^52,d^a=d^2e^3,e^a=d^6e^5,d^b=d^4e^4,e^b=e^21028 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31164, 60);