Finite Group DatabasebetaFinite Group Databasebeta| order | 19216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×#23751199 |
| Fitting, socle | C2×C1201 ⋊ C8 |
| derived, Sylow | C1201 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #23751199 |
| commutator, hypocenter | C1201 | C2×C8 |
| Frattini | C1 | G |
| Fitting, socle | C2×C1201 | C8 |
| prime radical | C2×D1201 | C4 |
| cosocle | #18012450 | C22 |
| LCS | G ▷ C1201 | |
| UCS | C1 ◁ C2 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2402 |
316 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#23751199, C22⋊#23751199, C4⋊#23751199, … |
| maximal normal subgroup of | C4×#23751199, C22⋊#23751199, C4⋊#23751199, … |
| maximal quotient of | C4×#23751199, C22⋊#23751199, C4⋊#23751199, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19216, 53);