Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#67290 |
| Fitting | C22×D4×C23 ⋊ C2 |
| Sylow | C23 ⋊ C22×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D23 |
| commutator, cosocle | C2×C23 | C25 |
| Frattini | C2 | C24×D23 |
| Fitting | C22×D4×C23 | C2 |
| socle | C23×C23 | C23 |
| hypercenter | C22×D4 | D23 |
| hypocenter | C23 | C22×#41 |
| LCS | G ▷ C2×C23 ▷ C23 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
890 conjugacy classes of subgroups.
| transitive degree | μt(G) = 736 |
260 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15673313, #15673322, #15673334, … |
| maximal normal subgroup of | #15673313, #15673322, #15673334, … |
| maximal quotient of | C22×#10625048, C22×#10625063, C22×(C22⋊D23)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 1375);