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C7×C23×C11⋊AGL(1,𝔽5) #47978443

order35420
automorphism?
homologyAbelianization (H1) = C4×C7×C23 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, socle, HallC5×C7×C11×C23 ⋊ C4
derived, HallC5×C11 ⋊ C4×C7×C23
HallC7×C11×C23 ⋊ AGL(1,𝔽5)
HallC5×C11×C23 ⋊ C4×C7
HallC5×C7×C23 ⋊ Dic11
HallC5×C7×C11 ⋊ C4×C23
HallC11×C23 ⋊ C7×AGL(1,𝔽5)
HallC5×C23 ⋊ C7×Dic11
HallC7×C11 ⋊ AGL(1,𝔽5)×C23
HallC5×C7 ⋊ C23×Dic11
SylowC11 ⋊ C7×AGL(1,𝔽5)×C23
SylowC5 ⋊ C7×C23×Dic11

Subgroups

subgroupG/H
center, hypercenterC7×C23C11⋊AGL(1,𝔽5)
commutator, hypocenterC5×C11C4×C7×C23
FrattiniC1G
Fitting, socleC5×C7×C11×C23C4
prime radicalC7×D5×C11×C23C2
cosocleD5×C11C2×C7×C23
LCSG ▷ C5×C11
UCSC1 ◁ C7×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8855

Conjugacy classes & character table

4025 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 77);