Finite Group Databasebeta

← Prev (#28412963) Next (#28412965) →

C3×C5×C49⋊AGL(1,𝔽5) #28412964

order14700
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C49⋊AGL(1,𝔽5)

Splittings

Fitting, HallC3×C52×C49 ⋊ C4
derivedC5×C49 ⋊ C3×C4×C5
HallC52×C49 ⋊ C3×C4
HallC3×C49 ⋊ C5×AGL(1,𝔽5)
HallC3×C52 ⋊ Dic49
SylowC49 ⋊ C3×C5×AGL(1,𝔽5)
SylowC52 ⋊ C3×Dic49

Subgroups

subgroupG/H
center, hypercenterC3×C5C49⋊AGL(1,𝔽5)
commutator, hypocenterC5×C49C3×C4×C5
FrattiniC7C3×C5×C7⋊AGL(1,𝔽5)
FittingC3×C52×C49C4
socleC3×C52×C7Dic7
prime radicalC3×C5×C7×D5D7
cosocleD5×C49C2×C3×C5
LCSG ▷ C5×C49
UCSC1 ◁ C3×C5

78 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1515 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 143);