Finite Group Databasebeta

← Prev (#26045406) Next (#26045408) →

C5×C17×C7⋊AGL(1,𝔽5) #26045407

order11900
isoclinismisoclinic class of C7⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC5×C17×C7⋊AGL(1,𝔽5)
unambiguous semidirect productC7⋊(C5×C17×AGL(1,𝔽5))

Splittings

Fitting, socle, HallC52×C7×C17 ⋊ C4
derivedC5×C7 ⋊ C4×C5×C17
HallC52×C17 ⋊ Dic7
HallC52×C7 ⋊ C4×C17
HallC7×C17 ⋊ C5×AGL(1,𝔽5)
SylowC52 ⋊ C17×Dic7
SylowC7 ⋊ C5×C17×AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC5×C17C7⋊AGL(1,𝔽5)
commutator, hypocenterC5×C7C4×C5×C17
FrattiniC1G
Fitting, socleC52×C7×C17C4
prime radicalC5×C7×D5×C17C2
cosocleC7×D5C2×C5×C17
LCSG ▷ C5×C7
UCSC1 ◁ C5×C17

52 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1445 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C17×ΓL(1,𝔽8)⋊AGL(1,𝔽5), C3×C5×C17×C7⋊AGL(1,𝔽5), C5×C17×C3⋊(C7⋊AGL(1,𝔽5))
maximal normal subgroup ofC5×C17×ΓL(1,𝔽8)⋊AGL(1,𝔽5), C3×C5×C17×C7⋊AGL(1,𝔽5)
maximal quotient ofC3×C5×C17×C7⋊AGL(1,𝔽5), C5×C17×C3⋊(C7⋊AGL(1,𝔽5))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11900, 56);