Finite Group DatabasebetaFinite Group Databasebeta| order | 1312 |
| isoclinism | isoclinic class of #4223 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C41 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | #4223 |
| commutator, hypocenter | C41 | C32 |
| Fitting | C8×C41 | C4 |
| socle, prime radical | C2×C41 | C16 |
| cosocle | #10620268 | C2 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C8 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 73 |
| transitive degree | μt(G) = 1312 |
Polycyclic presentation:
2^5,41|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^32,f^b=f^40112 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13050214, #14581267, #14581268, … |
| maximal normal subgroup of | C2×#13050214, #14581267, #14581268, … |
| maximal quotient of | #14581175, C2×#13050214 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1312, 196);