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C23×C7⋊(Dic11⋊C5) #47978397

order35420
automorphism?
homologyAbelianization (H1) = C4×C5×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×C7⋊(Dic11⋊C5)
unambiguous semidirect productC7⋊(C23×Dic11⋊C5)
unambiguous semidirect product(C11⋊C5)⋊(C23×Dic7)
unambiguous semidirect productDic77⋊(C5×C23)
unambiguous semidirect product(C23×Dic77)⋊C5

Splittings

derived, HallC7×C11 ⋊ C4×C5×C23
HallC7×C23×C11⋊C5 ⋊ C4
HallC23×Dic77 ⋊ C5
HallC7×C11×C23 ⋊ C4×C5
HallC23×C11⋊C5 ⋊ Dic7
HallC7×C11⋊C5 ⋊ C4×C23
HallDic77 ⋊ C5×C23
HallC11×C23 ⋊ C5×Dic7
HallC7×C23 ⋊ Dic11⋊C5
HallC11⋊C5 ⋊ C23×Dic7
SylowC11 ⋊ C5×C23×Dic7
SylowC7 ⋊ C23×Dic11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C23C7⋊AGL(1,𝔽11)
commutator, hypocenterC7×C11C4×C5×C23
FrattiniC2C23×C7⋊AGL(1,𝔽11)
Fitting, socleC2×C7×C11×C23C2×C5
prime radicalC2×C7×C23×C11⋊C5C2
cosocleC2×C7×C11C2×C5×C23
LCSG ▷ C7×C11
UCSC1 ◁ C2×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7084

Conjugacy classes & character table

1472 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 31);