Finite Group DatabasebetaFinite Group Databasebeta| order | 2336 |
| isoclinism | isoclinic class of #64408 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C73 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | #64408 |
| commutator, hypocenter | C73 | C32 |
| Fitting | C8×C73 | C4 |
| socle, prime radical | C2×C73 | C16 |
| cosocle | #11924003 | C2 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C8 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^5,73|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^27,f^b=f^72176 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14556641, #17989518, #17989519, … |
| maximal normal subgroup of | C2×#14556641, #17989518, #17989519, … |
| maximal quotient of | #17989426, C2×#14556641 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2336, 196);