Finite Group DatabasebetaFinite Group Databasebeta| order | 3708 |
| isoclinism | isoclinic class of D103 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C32×D103 |
| Fitting, socle | C2×C32×C103 ⋊ C2 |
| derived, Sylow | C103 ⋊ C22×C32 |
| Hall | C32×C103 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D103 |
| commutator, cosocle, hypocenter | C103 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C103 | C2 |
| LCS | G ▷ C103 | |
| UCS | C1 ◁ C2×C32 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1854 |
954 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D5×D103, C2×C32×D515, C2×C32×C5×D103, … |
| maximal normal subgroup of | C2×C32×C5×D103, C2×C32×C7×D103 |
| maximal quotient of | C32×D5×D103, C2×C32×D515, C2×C32×C5×D103, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3708, 46);