Finite Group DatabasebetaFinite Group Databasebeta| order | 12100 |
| isoclinism | isoclinic class of #1044 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C112 · Schur multiplier (H2) = C5×C11 |
| direct product | C112×#1044 |
| Fitting, socle, Hall | C52×C112 ⋊ C4 |
| derived, Sylow | C52 ⋊ C4×C112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C112 | #1044 |
| commutator, hypocenter | C52 | C4×C112 |
| Frattini | C1 | G |
| Fitting, socle | C52×C112 | C4 |
| prime radical | C112×C5⋊D5 | C2 |
| cosocle | C5⋊D5 | C2×C112 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C112 | |
224 conjugacy classes of subgroups.
1210 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C112×#64480, #1044×C112⋊C3, C3×C112×#1044, … |
| maximal normal subgroup of | #1044×C112⋊C3, C3×C112×#1044 |
| maximal quotient of | C3×C112×#1044, C112×C3⋊#1044 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12100, 257);