Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of #11924299 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, Sylow | C72 ⋊ SL(2,𝔽3) |
| derived, Hall | #87658 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | #87658 | C3 |
| Fitting, socle | C72 | SL(2,𝔽3) |
| LCS | G ▷ #87658 | |
| UCS | C1 | |
22 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 28 |
Polycyclic presentation:
3,2^3,7^2|b^2=d,c^2=d,b^a=bcd,c^a=b,e^a=e^4f^2,c^b=cd,e^b=f,f^b=e^6,e^c=e^3f^5,f^c=e^5f^4,e^d=e^6,f^d=f^617 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 214);