Finite Group DatabasebetaFinite Group Databasebeta| order | 18272 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#22603732 |
| Fitting | C2×D4×C571 ⋊ C2 |
| Sylow | C571 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D571 |
| commutator, cosocle | C2×C571 | C24 |
| Frattini | C2 | C23×D571 |
| Fitting | C2×D4×C571 | C2 |
| socle | C22×C571 | C23 |
| hypercenter | C2×D4 | D571 |
| hypocenter | C571 | C2×#41 |
| LCS | G ▷ C2×C571 ▷ C571 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
164 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9136 |
2870 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49142238, #49142247, #49142259, … |
| maximal normal subgroup of | #49142238, #49142247, #49142259, … |
| maximal quotient of | C2×#32912650, C2×#32912652, C2×(C22⋊D571)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18272, 188);