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C7×(C23⋊C11)⋊AGL(1,𝔽5) #47978401

order35420
automorphism?
homologyAbelianization (H1) = C4×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC7×(C23⋊C11)⋊AGL(1,𝔽5)
unambiguous semidirect product(C23⋊C11)⋊(C7×AGL(1,𝔽5))
unambiguous semidirect product(C23⋊AGL(1,𝔽5))⋊(C7×C11)
unambiguous semidirect product(C7×C23⋊AGL(1,𝔽5))⋊C11

Splittings

Fitting, socle, HallC5×C7×C23 ⋊ C4×C11
derived, HallC5×C23 ⋊ C4×C7×C11
HallC5×C7×C23⋊C11 ⋊ C4
HallC7×C23⋊AGL(1,𝔽5) ⋊ C11
HallC7×C23⋊C11 ⋊ AGL(1,𝔽5)
HallC5×C23⋊C11 ⋊ C4×C7
HallC23⋊AGL(1,𝔽5) ⋊ C7×C11
HallC23⋊C11 ⋊ C7×AGL(1,𝔽5)
HallC7×C23 ⋊ C11×AGL(1,𝔽5)
HallC5×C7 ⋊ Dic23⋊C11
SylowC23 ⋊ C7×C11×AGL(1,𝔽5)
SylowC5 ⋊ C7×Dic23⋊C11

Subgroups

subgroupG/H
center, hypercenterC7(C23⋊C11)⋊AGL(1,𝔽5)
commutator, hypocenterC5×C23C4×C7×C11
FrattiniC1G
Fitting, socleC5×C7×C23C4×C11
prime radicalC7×D5×C23⋊C11C2
cosocleD5×C23C2×C7×C11
LCSG ▷ C5×C23
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 805

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 35);