Finite Group DatabasebetaFinite Group Databasebeta| order | 17768 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C2221 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #22580075 |
| commutator, hypocenter | C2221 | C8 |
| Fitting, socle, prime radical | C2×C2221 | C4 |
| cosocle | Dic2221 | C2 |
| LCS | G ▷ C2221 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17768 |
Polycyclic presentation:
2^3,2221|a^2=b,b^2=c,d^a=d^1431,d^b=d^22201118 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#31801773, D2221⋊C8, #48001116, … |
| maximal normal subgroup of | C2×#31801773, D2221⋊C8, #48001116, … |
| maximal quotient of | #48001110, C2×#31801773 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17768, 13);