Finite Group Databasebeta

C2×#28414059 #44442496

order29504
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productC2×#28414059

Splittings

FittingC2×D8×C461 ⋊ C2
SylowC461 ⋊ C2×D16

Subgroups

subgroupG/H
centerC22#20301486
commutator, cosocleC8×C461C23
FrattiniC8C22×D461
FittingC2×D8×C461C2
socleC22×C461D8
hypercenterC2×D8D461
hypocenterC461C2×D16
LCSG ▷ C8×C461 ▷ C4×C461 ▷ C2×C461 ▷ C461
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

98 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14752

Conjugacy classes & character table

3242 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29504, 969);