Finite Group Databasebeta

C2×#14557363 #17996388

order4736
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#14557363

Splittings

SylowC37 ⋊ C2×#368

Subgroups

subgroupG/H
centerC2×C4D296
commutatorC8×C37C22×C4
FrattiniC2×C8C22×D37
FittingC22×C16×C37C2
socleC22×C37#107
prime radicalC23×C37Q16
cosocleC2×C8×C37C23
hypercenterC22×C16D37
hypocenterC37C2×#368
LCSG ▷ C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2368

Conjugacy classes & character table

1196 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 6302);