Finite Group DatabasebetaFinite Group Databasebeta| order | 2152 |
| isoclinism | isoclinic class of D269 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C269 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D269 |
| commutator, hypocenter | C269 | C8 |
| Fitting, cosocle | C4×C269 | C2 |
| socle, prime radical | C2×C269 | C4 |
| LCS | G ▷ C269 | |
| UCS | C1 ◁ C4 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 277 |
| transitive degree | μt(G) = 2152 |
Polycyclic presentation:
2^3,269|a^2=b,b^2=c,d^a=d^268544 conjugacy classes — view the full character table.
| maximal subgroup of | C8×D269, C2×#14524130, #16864385, … |
| maximal normal subgroup of | C8×D269, C2×#14524130, #16864385, … |
| maximal quotient of | #16864377, C2×#14524130 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2152, 6);