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C2×C17×C13⋊(C52⋊C3) #45684174

order33150
automorphism?
homologyAbelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C5

Aliases

direct productC2×C17×C13⋊(C52⋊C3)
unambiguous semidirect product(C2×C13)⋊(C17×C52⋊C3)
unambiguous semidirect product(C2×C52)⋊(C17×C13⋊C3)
unambiguous semidirect product(C2×C13×C17)⋊(C52⋊C3)
unambiguous semidirect product(C2×C52×C17)⋊(C13⋊C3)

Splittings

Fitting, socle, HallC2×C52×C13×C17 ⋊ C3
derived, HallC52×C13 ⋊ C2×C3×C17
HallC52×C13×C17 ⋊ C2×C3
HallC2×C52×C17 ⋊ C13⋊C3
HallC2×C52×C13 ⋊ C3×C17
HallC2×C13×C17 ⋊ C52⋊C3
HallC52×C17 ⋊ C2×C13⋊C3
HallC13×C17 ⋊ C2×C52⋊C3
HallC2×C52 ⋊ C17×C13⋊C3
HallC2×C13 ⋊ C17×C52⋊C3
SylowC52 ⋊ C2×C17×C13⋊C3
SylowC13 ⋊ C2×C17×C52⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C17C13⋊(C52⋊C3)
commutator, cosocle, hypocenterC52×C13C2×C3×C17
FrattiniC1G
Fitting, socleC2×C52×C13×C17C3
LCSG ▷ C52×C13
UCSC1 ◁ C2×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6630

Conjugacy classes & character table

3774 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33150, 56);