Finite Group Databasebeta

C4×#16813709 #28407142

order14464
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#16813709

Splittings

SylowC113 ⋊ C4×#131

Subgroups

subgroupG/H
centerC2×C4C22×#90673
commutatorC2×C113C22×C42
FrattiniC22C23×#90673
FittingC4×D4×C113C4
socleC22×C113C23×C4
prime radicalC2×#14268646C22
cosocleC2×Dic113C24
hypercenterC4×D4#90673
hypocenterC113C4×#131
LCSG ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C4×D4

572 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

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(14464, 21078);