Finite Group Databasebeta

C2×#20298435 #28392874

order14464
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#20298435

Splittings

FittingC2×Q32×C113 ⋊ C2
SylowC113 ⋊ C2×SD64

Subgroups

subgroupG/H
centerC22#16813563
commutator, cosocleC16×C113C23
FrattiniC16C22×D113
FittingC2×Q32×C113C2
socleC22×C113D16
prime radicalC2×D1808C2
hypercenterC2×Q32D113
hypocenterC113C2×SD64
LCSG ▷ C16×C113 ▷ C8×C113 ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×Q32

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

Conjugacy classes & character table

1270 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 6810);