Finite Group Databasebeta

C2×#14558414 #18010303

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

Aliases

direct productC2×#14558414

Splittings

SylowC37 ⋊ C2×#344

Subgroups

subgroupG/H
centerC22(C2×#3866)⋊C4
commutatorC22×C37C2×C42
FrattiniC23C22×#3866
FittingC2×C22⋊C4×C37C4
socleC22×C37#95
prime radicalC24×C37C2×C4
cosocleC22×Dic37C23
hypercenterC2×C22⋊C4#3866
hypocenterC37C2×#344
LCSG ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1184

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 20217);