Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of #64425 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C7 |
No aliases for this group.
| derived, Sylow | C72 ⋊ C3×C8 |
| Hall | C7⋊(C7⋊C8) ⋊ C3 |
| Hall | #3862 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | #64425 |
| commutator, hypocenter | C72 | C3×C8 |
| Fitting, cosocle | C4×C72 | C2×C3 |
| socle | C2×C72 | C3×C4 |
| prime radical | C2×#3862 | C4 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C4 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
Polycyclic presentation:
2,3,2^2,7^2|a^2=c,c^2=d,e^a=e^6,f^a=f^6,e^b=e^4,f^b=f^256 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#64425, #72245215, #72245217, … |
| maximal normal subgroup of | C8×#64425, #72245215, #72245217, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 64);