Finite Group Databasebeta

C2×#14557581 #18003202

order4736
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14557581

Splittings

SylowC37 ⋊ C2×#430

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊D37
commutatorC4×C37C23×C4
FrattiniC2×C4C23×D37
FittingC22×M16×C37C2
socleC22×C37C2×C4⋊C4
prime radicalC24×C37Q8
cosocleC2×C4×C37C24
hypercenterC22×M16D37
hypocenterC37C2×#430
LCSG ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×M16

460 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1184

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, 13116);