Finite Group Databasebeta

C4×#11745263 #16827912

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

Aliases

direct productC4×#11745263

Splittings

FittingC2×C4×C8×C29 ⋊ C2
SylowC29 ⋊ C4×#131

Subgroups

subgroupG/H
centerC4×C8C2×D29
commutatorC2×C29C22×C42
FrattiniC2×C4C23×D29
FittingC2×C4×C8×C29C2
socleC22×C29C23×C4
prime radicalC2×#90805C22
cosocleC2×C4×C29C24
hypercenterC2×C4×C8D29
hypocenterC29C4×#131
LCSG ▷ C2×C29 ▷ C29
UCSC1 ◁ C4×C8 ◁ C2×C4×C8

572 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1856

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 12930);