Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C8 · Schur multiplier (H2) = C43 |
| direct product | C4×C8×Dic7 |
| derived, Sylow | C7 ⋊ C42×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4×C8 | D7 |
| commutator, hypocenter | C7 | C42×C8 |
| Frattini | C22×C4 | C22×D7 |
| Fitting | C2×C4×C7×C8 | C2 |
| socle, prime radical | C23×C7 | C22×C4 |
| cosocle | C22×C4×C7 | C23 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C2×C4×C8 | |
408 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #13240651, C82×Dic7, Dic7×#322, … |
| maximal normal subgroup of | #13240651, C82×Dic7, Dic7×#322, … |
| maximal quotient of | C82×Dic7, C4×C8×C7⋊C8, Dic7×#322, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 2267);