Finite Group Databasebeta

C2×#14557309 #17996186

order4736
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#14557309

Splittings

SylowC37 ⋊ C2×#346

Subgroups

subgroupG/H
centerC22×C8C2×D37
commutatorC2×C37C2×C4×C8
FrattiniC2×C8C22×D37
FittingC2×C4×C8×C37C2
socle, prime radicalC23×C37C2×C8
cosocleC2×C8×C37C23
hypercenterC2×C4×C8D37
hypocenterC37C2×#346
LCSG ▷ C2×C37 ▷ C37
UCSC1 ◁ C22×C8 ◁ C2×C4×C8

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4736

Conjugacy classes & character table

1232 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 6100);