Finite Group Databasebeta

C2×#28414112 #44442601

order29504
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24

Aliases

direct productC2×#28414112

Splittings

FittingC2×C42×C461 ⋊ C2
SylowC461 ⋊ C2×#126

Subgroups

subgroupG/H
centerC23C22×D461
commutator, cosocleC22×C461C24
FrattiniC22C23×D461
FittingC2×C42×C461C2
socleC23×C461C23
prime radicalC23×D461C22
hypercenterC2×C42D461
hypocenterC461C2×#126
LCSG ▷ C22×C461 ▷ C461
UCSC1 ◁ C23 ◁ C2×C42

246 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14752

Conjugacy classes & character table

7388 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29504, 1074);