Finite Group Databasebeta

C2×#14557275 #17993180

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

Aliases

direct productC2×#14557275

Splittings

SylowC37 ⋊ C2×#330

Subgroups

subgroupG/H
centerC23C22⋊Dic37
commutatorC2×C4×C37C22×C4
FrattiniC42C22×D37
FittingC2×#125×C37C2
socle, prime radicalC23×C37C22⋊C4
cosocleC42×C37C23
hypercenterC2×#125D37
hypocenterC37C2×#330
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#125

232 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4736

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 3094);