Finite Group DatabasebetaFinite Group Databasebeta| order | 1376 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×Q8×C43 ⋊ C2 |
| Sylow | C43 ⋊ 2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D43 |
| commutator, socle, cosocle | C2×C43 | C24 |
| Fitting | C2×Q8×C43 | C2 |
| hypercenter | C2×Q8 | D43 |
| hypocenter | C43 | 2−1+4 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2 ◁ C2×Q8 | |
146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 688 |
Polycyclic presentation:
2^5,43|b^2=e,c^2=e,b^a=be,d^a=de,c^b=ce,f^b=f^42,f^d=f^42227 conjugacy classes — view the full character table.
| maximal subgroup of | #14583071, #14583074, #14583081, … |
| maximal normal subgroup of | #14583071, #14583074, #14583081, … |
| maximal quotient of | #14583375, #14583377, #14583380, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1376, 194);