Finite Group Databasebeta

C2×#14271096 #16822725

order3712
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14271096

Splittings

SylowC29 ⋊ C2×#398

Subgroups

subgroupG/H
centerC24C22×D29
commutator, cosocleC23×C29C24
FrattiniC23C23×D29
FittingC22×C4⋊C4×C29C2
socle, prime radicalC24×C29C23
hypercenterC22×C4⋊C4D29
hypocenterC29C2×#398
LCSG ▷ C23×C29 ▷ C29
UCSC1 ◁ C24 ◁ C22×C4⋊C4

692 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3712

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 7743);