Finite Group DatabasebetaFinite Group Databasebeta| order | 13768 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C1721 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #20293721 |
| commutator, hypocenter | C1721 | C8 |
| Fitting, socle, prime radical | C2×C1721 | C4 |
| cosocle | Dic1721 | C2 |
| LCS | G ▷ C1721 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13768 |
Polycyclic presentation:
2^3,1721|a^2=b,b^2=c,d^a=d^473,d^b=d^1720868 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#28351869, #42118206, #42118207, … |
| maximal normal subgroup of | C2×#28351869, #42118206, #42118207, … |
| maximal quotient of | #42118201, C2×#28351869 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13768, 13);