Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C7 ⋊ #2546 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D7 |
| commutator, socle, prime radical, cosocle | C23×C7 | C24 |
| Fitting | C2×C7×C4⋊Q8 | C2 |
| hypercenter | C2×C4⋊Q8 | D7 |
| hypocenter | C7 | #2546 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊Q8 | |
540 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 189 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^7,7|a^2=e,b^2=eg,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^6,c^b=cg,h^c=h^6122 conjugacy classes — view the full character table.
| maximal subgroup of | #13251163, #13251203, #13251477, … |
| maximal normal subgroup of | #13251163, #13251203, #13251477, … |
| maximal quotient of | #13276073, #13276212, #13276966, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 15450);