Finite Group Databasebeta

C2×#28410496 #44417201

order29248
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#28410496

Splittings

SylowC457 ⋊ C2×SD32

Subgroups

subgroupG/H
centerC22#20300726
commutator, cosocleC8×C457C23
FrattiniC8C22×D457
Fitting, prime radicalC2×D8×C457C2
socleC22×C457D8
hypercenterC2×D8D457
hypocenterC457C2×SD32
LCSG ▷ C8×C457 ▷ C4×C457 ▷ C2×C457 ▷ C457
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14624

Conjugacy classes & character table

3214 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29248, 973);