Finite Group DatabasebetaFinite Group Databasebeta| order | 2152 |
| isoclinism | isoclinic class of #11761640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×#11761640 |
| unambiguous semidirect product | D269⋊C4 |
| Fitting, socle | C2×C269 ⋊ C4 |
| derived, Sylow | C269 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #11761640 |
| commutator, hypocenter | C269 | C2×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C269 | C4 |
| prime radical | C2×D269 | C2 |
| cosocle | D269 | C22 |
| LCS | G ▷ C269 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 538 |
142 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#11761640, C22⋊#11761640, C4⋊#11761640, … |
| maximal normal subgroup of | C4×#11761640, C22⋊#11761640, C4⋊#11761640, … |
| maximal quotient of | C4×#11761640, C22⋊#11761640, C4⋊#11761640, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2152, 14);