Finite Group DatabasebetaFinite Group Databasebeta| order | 13792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#20293801 |
| Fitting | C2×Q8×C431 ⋊ C2 |
| Sylow | C431 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D431 |
| commutator, cosocle | C2×C431 | C24 |
| Frattini | C2 | C23×D431 |
| Fitting | C2×Q8×C431 | C2 |
| socle | C22×C431 | C23 |
| hypercenter | C2×Q8 | D431 |
| hypocenter | C431 | C2×#41 |
| LCS | G ▷ C2×C431 ▷ C431 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
164 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6896 |
2170 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #42119042, #42119054, #42119059, … |
| maximal normal subgroup of | #42119042, #42119054, #42119059, … |
| maximal quotient of | C2×#28352147, C2×#28352151, C2×Q8×Dic431, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13792, 190);