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C3×C61×C7⋊AGL(1,𝔽5) #38785164

order25620
automorphism?
homologyAbelianization (H1) = C3×C4×C61 · Schur multiplier (H2) = C1

Aliases

direct productC3×C61×C7⋊AGL(1,𝔽5)

Splittings

Fitting, socle, HallC3×C5×C7×C61 ⋊ C4
derived, HallC5×C7 ⋊ C3×C4×C61
HallC5×C7×C61 ⋊ C3×C4
HallC3×C7×C61 ⋊ AGL(1,𝔽5)
HallC3×C5×C61 ⋊ Dic7
HallC7×C61 ⋊ C3×AGL(1,𝔽5)
HallC5×C61 ⋊ C3×Dic7
HallC3×C5×C7 ⋊ C4×C61
HallC3×C7 ⋊ AGL(1,𝔽5)×C61
HallC3×C5 ⋊ Dic7×C61
SylowC7 ⋊ C3×AGL(1,𝔽5)×C61
SylowC5 ⋊ C3×Dic7×C61

Subgroups

subgroupG/H
center, hypercenterC3×C61C7⋊AGL(1,𝔽5)
commutator, hypocenterC5×C7C3×C4×C61
FrattiniC1G
Fitting, socleC3×C5×C7×C61C4
prime radicalC3×C7×D5×C61C2
cosocleC7×D5C2×C3×C61
LCSG ▷ C5×C7
UCSC1 ◁ C3×C61

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6405

Conjugacy classes & character table

3111 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25620, 237);