Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of #11924328 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting, socle | C22×C72 ⋊ D3 |
| derived | C22⋊#3862 ⋊ C2 |
| Sylow | C72 ⋊ S4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C22⋊#3862 | C2 |
| Fitting, socle | C22×C72 | D3 |
| LCS | G ▷ C22⋊#3862 | |
| UCS | C1 | |
43 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 42 |
Polycyclic presentation:
2,3,2^2,7^2|b^a=b^2,c^a=cd,e^a=f,f^a=e,c^b=cd,d^b=c,e^b=e^4,f^b=f^255 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 243);