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C3×C7⋊(C71⋊AGL(1,𝔽5)) #44447232

order29820
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7⋊(C71⋊AGL(1,𝔽5))
unambiguous semidirect productC71⋊(C3×C7⋊AGL(1,𝔽5))

Splittings

Fitting, socle, HallC3×C5×C7×C71 ⋊ C4
derived, HallC5×C7×C71 ⋊ C3×C4
HallC3×C7×C71 ⋊ AGL(1,𝔽5)
HallC3×C5×C71 ⋊ Dic7
HallC7×C71 ⋊ C3×AGL(1,𝔽5)
HallC5×C71 ⋊ C3×Dic7
HallC3×C71 ⋊ C7⋊AGL(1,𝔽5)
HallC3×C5×C7 ⋊ Dic71
SylowC71 ⋊ C3×C7⋊AGL(1,𝔽5)
HallC5×C7 ⋊ C3×Dic71
HallC3×C7 ⋊ C71⋊AGL(1,𝔽5)
HallC3×C5 ⋊ Dic497
SylowC7 ⋊ C3×C71⋊AGL(1,𝔽5)
SylowC5 ⋊ C3×Dic497

Subgroups

subgroupG/H
center, hypercenterC3C7⋊(C71⋊AGL(1,𝔽5))
commutator, hypocenterC5×C7×C71C3×C4
FrattiniC1G
Fitting, socleC3×C5×C7×C71C4
prime radicalC3×C7×D5×C71C2
cosocleC7×D5×C71C2×C3
LCSG ▷ C5×C7×C71
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7455

Conjugacy classes & character table

2991 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 120);