Finite Group Databasebeta

C2×#14557301 #17994331

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

Aliases

direct productC2×#14557301

Splittings

SylowC37 ⋊ C2×#343

Subgroups

subgroupG/H
centerC23#10596938
commutatorC22×C37C2×C42
FrattiniC22×C4C22×D37
FittingC22×M16×C37C2
socleC23×C37C22⋊C4
prime radicalC24×C37C2×C4
cosocleC22×C4×C37C23
hypercenterC22×M16D37
hypocenterC37C2×#343
LCSG ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×M16

432 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2368

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, 4245);