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C17×(C11⋊C5)⋊Dic5 #34035166

order18700
automorphism?
homologyAbelianization (H1) = C4×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×(C11⋊C5)⋊Dic5
unambiguous semidirect product(C11⋊C5)⋊(C17×Dic5)
unambiguous semidirect productDic55⋊(C5×C17)
unambiguous semidirect product(C17×Dic55)⋊C5

Splittings

derivedC5×C11 ⋊ C4×C5×C17
HallC5×C17×C11⋊C5 ⋊ C4
HallC5×C11⋊C5 ⋊ C4×C17
HallC11×C17 ⋊ C5×Dic5
SylowC11 ⋊ C5×C17×Dic5

Subgroups

subgroupG/H
center, hypercenterC2×C17C5⋊AGL(1,𝔽11)
commutator, hypocenterC5×C11C4×C5×C17
FrattiniC2C17×C5⋊AGL(1,𝔽11)
Fitting, socleC2×C5×C11×C17C2×C5
prime radicalC2×C5×C17×C11⋊C5C2
cosocleC2×C5×C11C2×C5×C17
LCSG ▷ C5×C11
UCSC1 ◁ C2×C17

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3740

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18700, 51);