Finite Group Databasebeta

C2×D4×#11744751 #28399247

order14464
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×D4×#11744751

Splittings

SylowC113 ⋊ C2×C8×D4

Subgroups

subgroupG/H
centerC22×C4C22×D113
commutatorC2×C113C23×C8
FrattiniC2×C4C23×D113
FittingC2×C4×D4×C113C2
socleC23×C113C22×C4
prime radicalC22×D4×C113C4
cosocleC2×C4×C113C24
hypercenterC2×C4×D4D113
hypocenterC113C2×C8×D4
LCSG ▷ C2×C113 ▷ C113
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

616 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

Conjugacy classes & character table

2320 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 13183);