Finite Group Databasebeta

C2×#14557456 #17997817

order4736
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#14557456

Splittings

SylowC37 ⋊ C2×#396

Subgroups

subgroupG/H
centerC24C22×D37
commutator, cosocleC23×C37C24
FrattiniC23C23×D37
FittingC22×C22⋊C4×C37C2
socleC24×C37C23
prime radicalC25×C37C22
hypercenterC22×C22⋊C4D37
hypocenterC37C2×#396
LCSG ▷ C23×C37 ▷ C37
UCSC1 ◁ C24 ◁ C22×C22⋊C4

908 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2368

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 7731);