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C11×C23×C7⋊AGL(1,𝔽5) #47978445

order35420
automorphism?
homologyAbelianization (H1) = C4×C11×C23 · Schur multiplier (H2) = C1

Aliases

direct productC11×C23×C7⋊AGL(1,𝔽5)
unambiguous semidirect productC7⋊(C11×AGL(1,𝔽5)×C23)

Splittings

Fitting, socle, HallC5×C7×C11×C23 ⋊ C4
derived, HallC5×C7 ⋊ C4×C11×C23
HallC7×C11×C23 ⋊ AGL(1,𝔽5)
HallC5×C11×C23 ⋊ Dic7
HallC5×C7×C23 ⋊ C4×C11
HallC5×C7×C11 ⋊ C4×C23
HallC7×C23 ⋊ C11×AGL(1,𝔽5)
HallC5×C23 ⋊ C11×Dic7
HallC7×C11 ⋊ AGL(1,𝔽5)×C23
HallC5×C11 ⋊ C23×Dic7
SylowC7 ⋊ C11×AGL(1,𝔽5)×C23
SylowC5 ⋊ C11×C23×Dic7

Subgroups

subgroupG/H
center, hypercenterC11×C23C7⋊AGL(1,𝔽5)
commutator, hypocenterC5×C7C4×C11×C23
FrattiniC1G
Fitting, socleC5×C7×C11×C23C4
prime radicalC7×D5×C11×C23C2
cosocleC7×D5C2×C11×C23
LCSG ▷ C5×C7
UCSC1 ◁ C11×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8855

Conjugacy classes & character table

4301 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 79);