Finite Group Databasebeta

C2×#20298582 #28399049

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

Aliases

direct productC2×#20298582

Splittings

SylowC113 ⋊ C2×#413

Subgroups

subgroupG/H
centerC2×C4C22⋊Dic113
commutatorC22×C113C23×C4
FrattiniC2×C4C23×D113
Fitting, prime radicalC22×#41×C113C2
socleC22×C113C2×C22⋊C4
cosocleC2×C4×C113C24
hypercenterC22×#41D113
hypocenterC113C2×#413
LCSG ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#41

756 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3616

Conjugacy classes & character table

2284 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 12985);