Finite Group DatabasebetaFinite Group Databasebeta| order | 14272 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C223 · Schur multiplier (H2) = C25 |
| direct product | C2×C4⋊Q8×C223 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C223 | C23 |
| commutator, Frattini, cosocle | C22 | C24×C223 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C223 ◁ G | |
290 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14272 |
6244 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#332×C223, C2×#333×C223, #1546×C223, … |
| maximal normal subgroup of | C2×#332×C223, C2×#333×C223, #1546×C223, … |
| maximal quotient of | C2×#384×C223, C2×#389×C223, C2×#391×C223, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14272, 212);