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C17×C7⋊(Dic11⋊C5) #39910401

order26180
automorphism?
homologyAbelianization (H1) = C4×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×C7⋊(Dic11⋊C5)
unambiguous semidirect productC7⋊(C17×Dic11⋊C5)
unambiguous semidirect product(C11⋊C5)⋊(C17×Dic7)
unambiguous semidirect productDic77⋊(C5×C17)
unambiguous semidirect product(C17×Dic77)⋊C5

Splittings

derived, HallC7×C11 ⋊ C4×C5×C17
HallC7×C17×C11⋊C5 ⋊ C4
HallC17×Dic77 ⋊ C5
HallC7×C11×C17 ⋊ C4×C5
HallC17×C11⋊C5 ⋊ Dic7
HallC7×C11⋊C5 ⋊ C4×C17
HallDic77 ⋊ C5×C17
HallC11×C17 ⋊ C5×Dic7
HallC7×C17 ⋊ Dic11⋊C5
HallC11⋊C5 ⋊ C17×Dic7
SylowC11 ⋊ C5×C17×Dic7
SylowC7 ⋊ C17×Dic11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C17C7⋊AGL(1,𝔽11)
commutator, hypocenterC7×C11C4×C5×C17
FrattiniC2C17×C7⋊AGL(1,𝔽11)
Fitting, socleC2×C7×C11×C17C2×C5
prime radicalC2×C7×C17×C11⋊C5C2
cosocleC2×C7×C11C2×C5×C17
LCSG ▷ C7×C11
UCSC1 ◁ C2×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5236

Conjugacy classes & character table

1088 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26180, 23);