Finite Group DatabasebetaFinite Group Databasebeta| order | 11172 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C72×C19 ⋊ C3×C4 |
| Hall | C72×Dic19 ⋊ C3 |
| Hall | #14584116 ⋊ C4 |
| Hall | Dic19 ⋊ #3861 |
| Sylow | C72 ⋊ (C19⋊C3)⋊C4 |
| Sylow | C19 ⋊ C4×#3861 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #19150312 |
| commutator, hypocenter | C72×C19 | C3×C4 |
| Fitting, socle, cosocle | C2×C72×C19 | C2×C3 |
| prime radical | C2×#14584116 | C2 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C2 | |
120 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7^2,19,2|a^2=f,e^a=e^18,c^b=c^2,d^b=d^2,e^b=e^11370 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11172, 107);