Finite Group Databasebeta

← Prev (#20269346) Next (#20269348) →

C5×C67⋊AGL(1,𝔽5) #20269347

order6700
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C67⋊AGL(1,𝔽5)
unambiguous semidirect productC67⋊(C5×AGL(1,𝔽5))

Splittings

Fitting, socle, HallC52×C67 ⋊ C4
derivedC5×C67 ⋊ C4×C5
SylowC67 ⋊ C5×AGL(1,𝔽5)
SylowC52 ⋊ Dic67

Subgroups

subgroupG/H
center, hypercenterC5C67⋊AGL(1,𝔽5)
commutator, hypocenterC5×C67C4×C5
FrattiniC1G
Fitting, socleC52×C67C4
LCSG ▷ C5×C67
UCSC1 ◁ C5

26 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

685 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×(C67⋊C3)⋊AGL(1,𝔽5), C3×C5×C67⋊AGL(1,𝔽5), C5×C3⋊(C67⋊AGL(1,𝔽5))
maximal normal subgroup ofC5×(C67⋊C3)⋊AGL(1,𝔽5), C3×C5×C67⋊AGL(1,𝔽5)
maximal quotient ofC3×C5×C67⋊AGL(1,𝔽5), C5×C3⋊(C67⋊AGL(1,𝔽5))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6700, 20);