Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C38 |
| direct product | H(3,𝔽3)×C32⋊(C37⋊C3) |
| Fitting | C32×H(3,𝔽3)×C37 ⋊ C3 |
| Sylow | C37 ⋊ H(3,𝔽3)2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C33×C37⋊C3 |
| commutator, socle, cosocle | C32×C37 | C34 |
| Fitting | C32×H(3,𝔽3)×C37 | C3 |
| hypercenter | C32×H(3,𝔽3) | C37⋊C3 |
| hypocenter | C37 | H(3,𝔽3)2 |
| LCS | G ▷ C32×C37 ▷ C37 | |
| UCS | C1 ◁ C32 ◁ C32×H(3,𝔽3) | |
2102 conjugacy classes of subgroups; only the 316 normal subgroups are shown.
This group has 2102 conjugacy classes of subgroups — too many to draw. Only its 316 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2997 |
1309 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 3566);