Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| isoclinism | isoclinic class of Dic14 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C24×C22⋊D7 |
| Fitting | C26×C7 ⋊ C2 |
| Sylow | C7 ⋊ C24×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C25 | C2×D7 |
| commutator, cosocle | C2×C7 | C26 |
| Frattini | C2 | C25×D7 |
| Fitting | C26×C7 | C2 |
| socle | C25×C7 | C22 |
| hypercenter | C26 | D7 |
| hypocenter | C7 | C24×D4 |
| LCS | G ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C25 ◁ C26 | |
10552 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
272 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#11729304, #13275662, #13275663, … |
| maximal normal subgroup of | C2×#11729304, #13275662, #13275663, … |
| maximal quotient of | C24×(C2×D7)⋊C4, C24×C22⋊Dic7, C24×Dic7⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19334);