Finite Group Databasebeta

C2×#28410546 #44417302

order29248
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24

Aliases

direct productC2×#28410546

Splittings

FittingC2×C42×C457 ⋊ C2
SylowC457 ⋊ C2×#126

Subgroups

subgroupG/H
centerC23C22×D457
commutator, cosocleC22×C457C24
FrattiniC22C23×D457
FittingC2×C42×C457C2
socleC23×C457C23
prime radicalC23×D457C22
hypercenterC2×C42D457
hypocenterC457C2×#126
LCSG ▷ C22×C457 ▷ C457
UCSC1 ◁ C23 ◁ C2×C42

246 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14624

Conjugacy classes & character table

7324 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29248, 1074);