Finite Group DatabasebetaFinite Group Databasebeta| order | 18425 |
| automorphism | ? |
| homology | Abelianization (H1) = C52×C11 · Schur multiplier (H2) = C5 |
| direct product | C52×C67⋊C11 |
| unambiguous semidirect product | C67⋊(C52×C11) |
| unambiguous semidirect product | (C5×C67)⋊(C5×C11) |
| unambiguous semidirect product | (C52×C67)⋊C11 |
| Fitting, socle, Hall | C52×C67 ⋊ C11 |
| derived, Sylow | C67 ⋊ C52×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | C67⋊C11 |
| commutator, cosocle, hypocenter | C67 | C52×C11 |
| Frattini | C1 | G |
| Fitting, socle | C52×C67 | C11 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C52 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1675 |
425 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×D67⋊C11, C5×C5⋊(D67⋊C11), C5×D5×C67⋊C11, … |
| maximal normal subgroup of | C52×D67⋊C11, C5×C5⋊(D67⋊C11), C5×D5×C67⋊C11, … |
| maximal quotient of | C2×C52×C67⋊C11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18425, 5);