Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | #3862 ⋊ Q8 |
| Sylow | C72 ⋊ Dic6 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#64418 |
| commutator, prime radical, cosocle | C2×#3862 | C22 |
| Fitting | C4×C72 | D3 |
| socle | C2×C72 | C2×D3 |
| hypercenter | C4 | #64418 |
| hypocenter | #3862 | Q8 |
| LCS | G ▷ C2×#3862 ▷ #3862 | |
| UCS | C1 ◁ C2 ◁ C4 | |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 56 |
Polycyclic presentation:
2^3,3,7^2|a^2=c,b^2=c,b^a=bc,d^a=d^2,e^a=e^4f,f^a=e^6f^3,e^d=e^2f^6,f^d=f^459 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 98);