Finite Group Databasebeta

C2×#28409074 #44408319

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

Aliases

direct productC2×#28409074

Splittings

SylowC227 ⋊ C2×#428

Subgroups

subgroupG/H
centerC23C2×D908
commutatorC4×C227C23×C4
FrattiniC2×C4C23×D227
FittingC22×M16×C227C2
socleC23×C227C2×D4
prime radicalC24×C227D4
cosocleC2×C4×C227C24
hypercenterC22×M16D227
hypocenterC227C2×#428
LCSG ▷ C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×M16

536 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14528

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, 13095);