Finite Group Databasebeta

C4×#11745269 #16827916

order3712
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#11745269

Splittings

FittingC4×M16×C29 ⋊ C2
SylowC29 ⋊ C4×#131

Subgroups

subgroupG/H
centerC42C22×D29
commutatorC2×C29C22×C42
FrattiniC2×C4C23×D29
FittingC4×M16×C29C2
socleC22×C29C23×C4
prime radicalC2×#90805C22
cosocleC2×C4×C29C24
hypercenterC4×M16D29
hypocenterC29C4×#131
LCSG ▷ C2×C29 ▷ C29
UCSC1 ◁ C42 ◁ C4×M16

572 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1856

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 12934);