Finite Group DatabasebetaFinite Group Databasebeta| order | 18896 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | C4×Dic1181 |
| derived, Sylow | C1181 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D1181 |
| commutator, hypocenter | C1181 | C42 |
| Frattini | C22 | C2×D1181 |
| Fitting | C2×C4×C1181 | C2 |
| socle, prime radical, cosocle | C22×C1181 | C22 |
| LCS | G ▷ C1181 | |
| UCS | C1 ◁ C2×C4 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18896 |
4736 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×Dic1181, #49180313, #49180329, … |
| maximal normal subgroup of | C8×Dic1181, #49180313, #49180329, … |
| maximal quotient of | #49180310, C8×Dic1181, C4×#22628129, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18896, 16);