Finite Group DatabasebetaFinite Group Databasebeta| order | 12100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C112 ⋊ C4×C25 |
| Hall | #15690027 ⋊ C4 |
| Hall | C11×Dic11 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C5 | #11925895 |
| commutator, hypocenter | C112 | C4×C25 |
| Fitting, socle, prime radical, cosocle | C2×C5×C112 | C2×C5 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C2×C5 | |
66 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,11^2,2,5|a^2=e,b^5=f,c^a=c^10,c^b=c^4,d^b=d^4250 conjugacy classes — view the full character table.
| maximal subgroup of | #13089712⋊C25, C3×#27130779, C3⋊#27130779 |
| maximal normal subgroup of | C3×#27130779 |
| maximal quotient of | C3×#27130779, C3⋊#27130779 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12100, 58);