Finite Group Databasebeta

C2×D113⋊#104 #28407198

order14464
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×D113⋊#104
unambiguous semidirect productD113⋊(C2×#104)

Splittings

FittingC2×#41×C113 ⋊ C4
SylowC113 ⋊ C22×#104

Subgroups

subgroupG/H
centerC2×C4C22⋊#90673
commutatorC4×C113C23×C4
FrattiniC4C23×#90673
FittingC2×#41×C113C4
socleC22×C113C2×C22⋊C4
prime radicalC2×#41×D113C2
cosocleC4×D113C24
hypercenterC2×#41#90673
hypocenterC113C22×#104
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

856 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1808

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 21134);