Finite Group Databasebeta

C2×#28408869 #44402034

order29056
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#28408869

Splittings

FittingC2×Q32×C227 ⋊ C2
SylowC227 ⋊ C2×SD64

Subgroups

subgroupG/H
centerC22#20300229
commutator, cosocleC16×C227C23
FrattiniC16C22×D227
FittingC2×Q32×C227C2
socleC22×C227D16
prime radicalC2×D3632C2
hypercenterC2×Q32D227
hypocenterC227C2×SD64
LCSG ▷ C16×C227 ▷ C8×C227 ▷ C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×Q32

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14528

Conjugacy classes & character table

2524 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 6810);