Finite Group Databasebeta

C2×#28409152 #44408628

order29056
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#28409152

Splittings

FittingC2×#131×C227 ⋊ C2
SylowC227 ⋊ C2×#444

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊D227
commutatorC4×C227C23×C4
FrattiniC2×C4C23×D227
FittingC2×#131×C227C2
socleC22×C227C4×D4
prime radicalC2×#20300308C2
cosocleC2×C4×C227C24
hypercenterC2×#131D227
hypocenterC227C2×#444
LCSG ▷ C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#131

464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7264

Conjugacy classes & character table

4564 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 13404);