Finite Group Databasebeta

C2×D113⋊#108 #28407231

order14464
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×D113⋊#108
unambiguous semidirect productD113⋊(C2×#108)

Splittings

SylowC113 ⋊ C22×#108

Subgroups

subgroupG/H
centerC2×C4C4⋊#90673
commutatorC4×C113C23×C4
FrattiniC4C23×#90673
FittingC22×C8×C113C4
socleC22×C113C2×C4⋊C4
prime radicalC23×D113Q8
cosocleC4×D113C24
hypercenterC22×C8#90673
hypocenterC113C22×#108
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3616

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 21167);