Finite Group Databasebeta

C2×#28414137 #44442855

order29504
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#28414137

Splittings

FittingC2×D8×C461 ⋊ C2
SylowC461 ⋊ C2×#135

Subgroups

subgroupG/H
centerC22D4×D461
commutator, cosocleC4×C461C24
FrattiniC4C23×D461
FittingC2×D8×C461C2
socleC22×C461C2×D4
hypercenterC2×D8D461
hypocenterC461C2×#135
LCSG ▷ C4×C461 ▷ C2×C461 ▷ C461
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14752

Conjugacy classes & character table

3248 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29504, 1328);