Finite Group Databasebeta

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C7×C25×C3⋊AGL(1,𝔽7) #36347742

order22050
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C25 · Schur multiplier (H2) = C1

Aliases

direct productC7×C25×C3⋊AGL(1,𝔽7)
unambiguous semidirect productC3⋊(C7×C25×AGL(1,𝔽7))
unambiguous semidirect productΓL(1,𝔽8)⋊(D3×C7×C25)
unambiguous semidirect productD21⋊(C3×C7×C25)
unambiguous semidirect product(C25×D21)⋊(C3×C7)

Splittings

FittingC3×C72×C25 ⋊ C2×C3
derivedC3×C7 ⋊ C2×C3×C7×C25
HallC3×C7×ΓL(1,𝔽8)×C25 ⋊ C2
HallC72×C25 ⋊ C3×D3
HallC3×C7×ΓL(1,𝔽8) ⋊ C2×C25
SylowC72 ⋊ C3×D3×C25

Subgroups

subgroupG/H
center, hypercenterC7×C25C3⋊AGL(1,𝔽7)
commutator, hypocenterC3×C7C2×C3×C7×C25
FrattiniC5C5×C7×C3⋊AGL(1,𝔽7)
FittingC3×C72×C25C2×C3
socleC3×C5×C72C2×C3×C5
prime radicalC5×C7×C3⋊AGL(1,𝔽7)C5
cosocleC3×C5×C7C2×C3×C5×C7
LCSG ▷ C3×C7
UCSC1 ◁ C7×C25

114 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 114 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3150

Conjugacy classes & character table

2100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22050, 179);