Finite Group Databasebeta

C2×#20299322 #28404124

order14464
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#20299322

Splittings

FittingC2×C4⋊Q8×C113 ⋊ C2
SylowC113 ⋊ C2×#556

Subgroups

subgroupG/H
centerC23C23×D113
commutator, cosocleC22×C113C25
FrattiniC22C24×D113
FittingC2×C4⋊Q8×C113C2
socleC23×C113C24
prime radicalC22×D452C22
hypercenterC2×C4⋊Q8D113
hypocenterC113C2×#556
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

1112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

Conjugacy classes & character table

1618 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 18060);