Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C7×#405 ⋊ C2 |
| Sylow | C7 ⋊ #2968 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D7 |
| commutator, socle | C22×C7 | C23×C4 |
| Fitting | C7×#405 | C2 |
| prime radical | #6447 | C4 |
| cosocle | C2×C4×C7 | C24 |
| hypercenter | #405 | D7 |
| hypocenter | C7 | #2968 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C2×C4 ◁ #405 | |
372 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=f,c^2=f,d^2=e,f^2=g,b^a=be,h^b=h^6,d^c=dg170 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#2968, C2×#11736003, #14218333, … |
| maximal normal subgroup of | D7×#2968, C2×#11736003, #14218333, … |
| maximal quotient of | #13352060, #13352068, #13352093, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 10769);