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C5×AGL(1,𝔽5)×C67 #20269346

order6700
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C5×C67 · Schur multiplier (H2) = C1

Aliases

direct productC5×AGL(1,𝔽5)×C67

Splittings

Fitting, socle, HallC52×C67 ⋊ C4
derivedC5 ⋊ C4×C5×C67
SylowC52 ⋊ C4×C67

Subgroups

subgroupG/H
center, hypercenterC5×C67AGL(1,𝔽5)
commutator, hypocenterC5C4×C5×C67
FrattiniC1G
Fitting, socleC52×C67C4
LCSG ▷ C5
UCSC1 ◁ C5×C67

26 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1675 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×AGL(1,𝔽5)×C67⋊C3, C3×C5×AGL(1,𝔽5)×C67, C5×ΓL(1,𝔽16)×C67
maximal normal subgroup ofC5×AGL(1,𝔽5)×C67⋊C3, C3×C5×AGL(1,𝔽5)×C67
maximal quotient ofC3×C5×AGL(1,𝔽5)×C67, C5×ΓL(1,𝔽16)×C67

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6700, 19);