Finite Group Databasebeta

C4×#20301511 #44443038

order29504
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct productC4×#20301511

Splittings

SylowC461 ⋊ C4×M16

Subgroups

subgroupG/H
centerC2×C4C2×#14270406
commutatorC2×C461C2×C42
FrattiniC22C22×#14270406
FittingC42×C461C4
socleC22×C461C22×C4
prime radicalC22×D461C2×C4
cosocleC2×Dic461C23
hypercenterC42#14270406
hypocenterC461C4×M16
LCSG ▷ C2×C461 ▷ C461
UCSC1 ◁ C2×C4 ◁ C42

142 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14752

Conjugacy classes & character table

1880 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29504, 1511);