Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of #64418 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | #3862 ⋊ C8 |
| Sylow | C72 ⋊ C3⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | #64418 |
| commutator, hypocenter | #3862 | C8 |
| Fitting | C4×C72 | D3 |
| socle | C2×C72 | Dic3 |
| prime radical | C2×#3862 | C4 |
| cosocle | C4×#3862 | C2 |
| LCS | G ▷ #3862 | |
| UCS | C1 ◁ C4 | |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 56 |
Polycyclic presentation:
2^3,3,7^2|a^2=b,b^2=c,d^a=d^2,e^a=e^2f^3,f^a=e^6f^5,e^d=e^4f^4,f^d=f^280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 57);