Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #14519104 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C32 |
No aliases for this group.
| Fitting, derived, Sylow | H(5,𝔽3) ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | H(5,𝔽3) | C2×C4 |
| Frattini, socle | C3 | #10620198 |
| prime radical | #11758086 | C2 |
| cosocle | #92404 | C22 |
| LCS | G ▷ H(5,𝔽3) | |
| UCS | C1 | |
313 conjugacy classes of subgroups; only the 14 normal subgroups are shown.
This group has 313 conjugacy classes of subgroups — too many to draw. Only its 14 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 27 |
Polycyclic presentation:
2^3,3^5|a^2=c,d^a=de,e^a=de^2,f^a=fg,g^a=fg^2,d^b=d^2,e^b=e^2,h^b=h^2,d^c=d^2,e^c=e^2,f^c=f^2,g^c=g^2,g^d=gh^2,f^e=fh28 conjugacy classes — view the full character table.
| maximal subgroup of | #72244503, #72254095, #72254096 |
| maximal normal subgroup of | #72244503, #72254095, #72254096 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3498);