Finite Group Databasebeta

C2×#28409004 #44408189

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

Aliases

direct productC2×#28409004

Splittings

FittingC2×#99×C227 ⋊ C2
SylowC227 ⋊ C2×#410

Subgroups

subgroupG/H
centerC22C22⋊C4×D227
commutatorC22×C227C23×C4
FrattiniC23C23×D227
FittingC2×#99×C227C2
socleC22×C227C2×C22⋊C4
prime radicalC22×#16813883C2
cosocleC23×C227C24
hypercenterC2×#99D227
hypocenterC227C2×#410
LCSG ▷ C22×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

788 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7264

Conjugacy classes & character table

2530 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 12965);