Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#89513 |
| Fitting | C2×C7×#99 ⋊ C2 |
| Sylow | C7 ⋊ C2×B(4,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #6445 |
| commutator, cosocle | C23×C7 | C24 |
| Frattini | C23 | C23×D7 |
| Fitting | C2×C7×#99 | C2 |
| socle | C22×C7 | #120 |
| hypercenter | C2×#99 | D7 |
| hypocenter | C7 | C2×B(4,𝔽2) |
| LCS | G ▷ C23×C7 ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ C2×#99 | |
1018 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 1018 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 112 |
98 conjugacy classes — view the full character table.
| maximal subgroup of | #13271055, #13271057, #13271069, … |
| maximal normal subgroup of | #13271055, #13271057, #13271069, … |
| maximal quotient of | C2×#11726038, C2×#11725860, C2×#11726040, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 10895);