Finite Group Databasebeta

C2×#14557303 #17994337

order4736
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#14557303

Splittings

SylowC37 ⋊ C2×#344

Subgroups

subgroupG/H
centerC2×C4#10596938
commutatorC22×C37C2×C42
FrattiniC22×C4C22×D37
FittingC2×#117×C37C2
socleC22×C37#95
prime radicalC24×C37C2×C4
cosocleC22×C4×C37C23
hypercenterC2×#117D37
hypocenterC37C2×#344
LCSG ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1184

Conjugacy classes & character table

764 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 4251);