Finite Group Databasebeta

C2×#14271190 #16828051

order3712
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14271190

Splittings

SylowC29 ⋊ C2×#424

Subgroups

subgroupG/H
centerC22×C4C22×D29
commutatorC22×C29C23×C4
FrattiniC2×C4C23×D29
FittingC2×C29×#117C2
socleC23×C29C22×C4
prime radicalC24×C29C2×C4
cosocleC2×C4×C29C24
hypercenterC2×#117D29
hypocenterC29C2×#424
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C22×C4 ◁ C2×#117

512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1856

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 13069);