Finite Group Databasebeta

← Prev (#28413497) Next (#28413499) →

C5×C3⋊(C7⋊(C7⋊AGL(1,𝔽5))) #28413498

order14700
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C7

Aliases

direct productC5×C3⋊(C7⋊(C7⋊AGL(1,𝔽5)))
unambiguous semidirect productC3⋊(C5×C7⋊(C7⋊AGL(1,𝔽5)))
unambiguous semidirect productC7⋊(C5×C3⋊(C7⋊AGL(1,𝔽5)))

Splittings

Fitting, socle, HallC3×C52×C72 ⋊ C4
derivedC3×C5×C72 ⋊ C4×C5
HallC52×C72 ⋊ Dic3
HallC3×C72 ⋊ C5×AGL(1,𝔽5)
HallC3×C52 ⋊ C7⋊Dic7
SylowC72 ⋊ C5×ΓL(1,𝔽16)
SylowC52 ⋊ C3⋊(C7⋊Dic7)
SylowC3 ⋊ C5×C7⋊(C7⋊AGL(1,𝔽5))

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(C7⋊(C7⋊AGL(1,𝔽5)))
commutator, hypocenterC3×C5×C72C4×C5
FrattiniC1G
Fitting, socleC3×C52×C72C4
prime radicalC3×C5×C72×D5C2
cosocleC3×C72×D5C2×C5
LCSG ▷ C3×C5×C72
UCSC1 ◁ C5

260 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1485 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 677);