Finite Group DatabasebetaFinite Group Databasebeta| order | 14944 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#21418743 |
| Fitting | C22×C4×C467 ⋊ C2 |
| Sylow | C467 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D467 |
| commutator, cosocle | C2×C467 | C24 |
| Frattini | C2 | C23×D467 |
| Fitting | C22×C4×C467 | C2 |
| socle | C22×C467 | C23 |
| hypercenter | C22×C4 | D467 |
| hypocenter | C467 | C2×#41 |
| LCS | G ▷ C2×C467 ▷ C467 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 | |
164 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7472 |
3748 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44470002, #44470003, #44470005, … |
| maximal normal subgroup of | #44470002, #44470003, #44470005, … |
| maximal quotient of | C2×#28417910, C2×#28417912, C2×C4×C22⋊D467, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14944, 189);