Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #2369 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D7 |
| commutator | C22×C7 | C23×C4 |
| Fitting | C2×C7×C4⋊Q8 | C2 |
| socle, prime radical, cosocle | C23×C7 | C24 |
| hypercenter | C2×C4⋊Q8 | D7 |
| hypocenter | C7 | #2369 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊Q8 | |
496 conjugacy classes of subgroups; only the 261 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 261 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=g,b^2=f,c^2=fg,d^2=e,b^a=be,c^a=cfg,h^a=h^6,d^b=de,h^b=h^6134 conjugacy classes — view the full character table.
| maximal subgroup of | #13248253, #13248257, #13248260, … |
| maximal normal subgroup of | #13248253, #13248257, #13248260, … |
| maximal quotient of | #13275236, #13275346, #13275412, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 15441);