Finite Group DatabasebetaFinite Group Databasebeta| order | 24198 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C37×C109 ⋊ C2×C3 |
| Hall | #27130719 ⋊ C2 |
| Hall | C37×D109 ⋊ C3 |
| Hall | D109 ⋊ C37⋊C3 |
| Sylow | C109 ⋊ C2×C37⋊C3 |
| Sylow | C37 ⋊ D109⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C37×C109 | C2×C3 |
| LCS | G ▷ C37×C109 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4033 |
Polycyclic presentation:
2,3,37,109|d^a=d^108,c^b=c^26,d^b=d^63696 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24198, 15);