Finite Group DatabasebetaFinite Group Databasebeta| order | 2152 |
| isoclinism | isoclinic class of D269 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×Dic269 |
| derived, Sylow | C269 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D269 |
| commutator, hypocenter | C269 | C2×C4 |
| Frattini | C2 | C2×D269 |
| Fitting, socle, prime radical | C22×C269 | C2 |
| cosocle | C2×C269 | C22 |
| LCS | G ▷ C269 | |
| UCS | C1 ◁ C22 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2152 |
544 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×Dic269, #16864379, C22⋊Dic269, … |
| maximal normal subgroup of | C4×Dic269, #16864379, C22⋊Dic269, … |
| maximal quotient of | C4×Dic269, C22⋊Dic269, C4⋊Dic269, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2152, 8);