Finite Group Databasebeta

C2×#14557557 #18003151

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

Aliases

direct productC2×#14557557

Splittings

SylowC37 ⋊ C2×#423

Subgroups

subgroupG/H
centerC22×C4C22×D37
commutatorC22×C37C23×C4
FrattiniC2×C4C23×D37
FittingC22×C42×C37C2
socleC23×C37C22×C4
prime radicalC24×C37C2×C4
cosocleC2×C4×C37C24
hypercenterC22×C42D37
hypocenterC37C2×#423
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C22×C4 ◁ C22×C42

576 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2368

Conjugacy classes & character table

1208 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 13065);