Finite Group DatabasebetaFinite Group Databasebeta| order | 12100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5 |
No aliases for this group.
| derived, Hall | C5×#10597245 ⋊ C4 |
| Sylow | C112 ⋊ #1039 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊#11925890 |
| commutator, hypocenter | C5×#10597245 | C4 |
| Fitting, socle | C2×C5×C112 | D5 |
| prime radical, cosocle | C2×C5×#10597245 | C2 |
| LCS | G ▷ C5×#10597245 | |
| UCS | C1 ◁ C2 | |
76 conjugacy classes of subgroups.
Polycyclic presentation:
2,5^2,11^2,2|a^2=f,b^a=b^4,c^a=c^4,d^a=e,e^a=d,d^b=d^5,e^b=e^9178 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#27130863, C3⋊#27130863 |
| maximal normal subgroup of | C3×#27130863 |
| maximal quotient of | C3×#27130863, C3⋊#27130863 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12100, 142);