Finite Group DatabasebetaFinite Group Databasebeta| order | 10984 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C1373 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #19130055 |
| commutator, hypocenter | C1373 | C8 |
| Fitting, socle, prime radical | C2×C1373 | C4 |
| cosocle | Dic1373 | C2 |
| LCS | G ▷ C1373 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,1373|a^2=b,b^2=c,d^a=d^668,d^b=d^1372694 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#24926901, D1373⋊C8, #36347032, … |
| maximal normal subgroup of | C2×#24926901, D1373⋊C8, #36347032, … |
| maximal quotient of | #36347026, C2×#24926901 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10984, 13);