Finite Group Databasebeta

C2×#14271640 #16832682

order3712
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#14271640

Splittings

SylowC29 ⋊ C2×#519

Subgroups

subgroupG/H
centerC23C23×D29
commutatorC2×C29C24×C4
FrattiniC22C24×D29
FittingC2×C29×#117C2
socleC23×C29C24
prime radicalC24×C29C23
cosocleC22×C29C25
hypercenterC2×#117D29
hypocenterC29C2×#519
LCSG ▷ C2×C29 ▷ C29
UCSC1 ◁ C23 ◁ C2×#117

1488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1856

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 17700);