Finite Group Databasebeta

← Prev (#26045367) Next (#26045369) →

C17×C7⋊#1035 #26045368

order11900
automorphism?
homologyAbelianization (H1) = C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×C7⋊#1035
unambiguous semidirect productC7⋊(C17×#1035)

Splittings

Fitting, HallC7×C17×C25 ⋊ C4
derived, HallC7×C25 ⋊ C4×C17
HallC17×C25 ⋊ Dic7
HallC7×C17 ⋊ #1035
SylowC25 ⋊ C17×Dic7
SylowC7 ⋊ C17×#1035

Subgroups

subgroupG/H
center, hypercenterC17C7⋊#1035
commutator, hypocenterC7×C25C4×C17
FrattiniC5C17×C7⋊AGL(1,𝔽5)
FittingC7×C17×C25C4
socleC5×C7×C17AGL(1,𝔽5)
prime radicalC7×C17×D25C2
cosocleC7×D25C2×C17
LCSG ▷ C7×C25
UCSC1 ◁ C17

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

884 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC17×ΓL(1,𝔽8)⋊#1035, C3×C17×C7⋊#1035, C17×C3⋊(C7⋊#1035)
maximal normal subgroup ofC17×ΓL(1,𝔽8)⋊#1035, C3×C17×C7⋊#1035
maximal quotient ofC3×C17×C7⋊#1035, C17×C3⋊(C7⋊#1035)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11900, 17);