Finite Group DatabasebetaFinite Group Databasebeta| order | 872 |
| isoclinism | isoclinic class of D109 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C109 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D109 |
| commutator, hypocenter | C109 | C8 |
| Fitting, cosocle | C4×C109 | C2 |
| socle, prime radical | C2×C109 | C4 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C4 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 872 |
Polycyclic presentation:
2^3,109|a^2=b,b^2=c,d^a=d^108224 conjugacy classes — view the full character table.
| maximal subgroup of | C8×D109, C2×#11724784, #13182012, … |
| maximal normal subgroup of | C8×D109, C2×#11724784, #13182012, … |
| maximal quotient of | #13182004, C2×#11724784 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(872, 1);