Finite Group Databasebeta

C2×#104×D227 #44408269

order29056
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#104×D227

Splittings

FittingC2×#104×C227 ⋊ C2
SylowC227 ⋊ C22×#104

Subgroups

subgroupG/H
centerC2×C4D4×D227
commutatorC4×C227C23×C4
FrattiniC2×C4C23×D227
FittingC2×#104×C227C2
socleC22×C227C2×C22⋊C4
prime radicalC2×#41×D227C2
cosocleC2×C4×C227C24
hypercenterC2×#104D227
hypocenterC227C22×#104
LCSG ▷ C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

856 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3632

Conjugacy classes & character table

3220 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 13045);