Finite Group Databasebeta

C2×#14557371 #17996897

order4736
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#14557371

Splittings

SylowC37 ⋊ C2×SD64

Subgroups

subgroupG/H
centerC22#11924477
commutator, cosocleC16×C37C23
FrattiniC16C22×D37
Fitting, prime radicalC2×D16×C37C2
socleC22×C37D16
hypercenterC2×D16D37
hypocenterC37C2×SD64
LCSG ▷ C16×C37 ▷ C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×D16

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2368

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 6811);