Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of #13091503 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C34 |
No aliases for this group.
| Fitting, Sylow | H(3,𝔽3)2 ⋊ C2 |
| derived | C34 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C34 | C2×C32 |
| Frattini, socle | C32 | C32×C3⋊D3 |
| Fitting | H(3,𝔽3)2 | C2 |
| LCS | G ▷ C34 | |
| UCS | C1 | |
776 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 776 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 81 |
Polycyclic presentation:
2,3^6|b^a=b^2deg,c^a=c^2e^2f^2,f^a=f^2,g^a=g^2,c^b=cf,d^b=dg,e^c=ef74 conjugacy classes — view the full character table.
| maximal subgroup of | #72214331, (C3⋊D3)⋊C32, #72214370, … |
| maximal normal subgroup of | #72214331, (C3⋊D3)⋊C32, #72214370, … |
| maximal quotient of | #72221865, #72221878, C3×#13091503, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1577);