Finite Group DatabasebetaFinite Group Databasebeta| order | 34192 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D4×C2137 ⋊ C2 |
| Sylow | C2137 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D2137 |
| commutator, socle, cosocle | C2×C2137 | C23 |
| Fitting | D4×C2137 | C2 |
| hypercenter | D4 | D2137 |
| hypocenter | C2137 | #41 |
| LCS | G ▷ C2×C2137 ▷ C2137 | |
| UCS | C1 ◁ C2 ◁ D4 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17096 |
Polycyclic presentation:
2^4,2137|c^2=d,b^a=bd,e^c=e^21365350 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34192, 39);