Finite Group Databasebeta

C2×#14558220 #18008105

order4736
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#14558220

Splittings

SylowC37 ⋊ C2×#552

Subgroups

subgroupG/H
centerC23C23×D37
commutator, cosocleC22×C37C25
FrattiniC22C24×D37
FittingC2×#123×C37C2
socleC23×C37C24
prime radicalC22×D4×C37C22
hypercenterC2×#123D37
hypocenterC37C2×#552
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ C2×#123

1124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2368

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 18019);