Finite Group DatabasebetaFinite Group Databasebeta| order | 28816 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D4×C1801 ⋊ C2 |
| Sylow | C1801 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D1801 |
| commutator, socle, cosocle | C2×C1801 | C23 |
| Fitting | D4×C1801 | C2 |
| hypercenter | D4 | D1801 |
| hypocenter | C1801 | #41 |
| LCS | G ▷ C2×C1801 ▷ C1801 | |
| UCS | C1 ◁ C2 ◁ D4 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14408 |
Polycyclic presentation:
2^4,1801|c^2=d,b^a=bd,e^c=e^18004510 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28816, 39);