Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of #157⋊D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C32×C7 ⋊ C4⋊C4 |
| Sylow | C32 ⋊ C4⋊Dic7 |
| Sylow | C7 ⋊ #3773 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #157⋊D7 |
| commutator | C7×C3⋊D3 | C2×C4 |
| Fitting, socle | C2×C32×C7 | D4 |
| prime radical, cosocle | C2×C7×C3⋊D3 | C22 |
| hypocenter | C32×C7 | C4⋊C4 |
| LCS | G ▷ C7×C3⋊D3 ▷ C32×C7 | |
| UCS | C1 ◁ C2 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
Polycyclic presentation:
2^4,3^2,7|a^2=d,b^2=c,b^a=bc,e^a=e^2,g^a=g^6,e^b=f,f^b=e^2,e^c=e^2,f^c=f^254 conjugacy classes — view the full character table.
| maximal subgroup of | #72217594, Dic7×GO+(4,𝔽2), C4×#157⋊D7, … |
| maximal normal subgroup of | #72217594, Dic7×GO+(4,𝔽2), C4×#157⋊D7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 579);