Finite Group Databasebeta

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C2×C11×C17×C52⋊C3 #43242528

order28050
automorphism?
homologyAbelianization (H1) = C2×C3×C11×C17 · Schur multiplier (H2) = C5

Aliases

direct productC2×C11×C17×C52⋊C3
unambiguous semidirect product(C2×C52)⋊(C3×C11×C17)
unambiguous semidirect product(C2×C52×C11)⋊(C3×C17)
unambiguous semidirect product(C2×C52×C17)⋊(C3×C11)
unambiguous semidirect product(C2×C52×C11×C17)⋊C3

Splittings

Fitting, socle, HallC2×C52×C11×C17 ⋊ C3
derived, SylowC52 ⋊ C2×C3×C11×C17
HallC52×C11×C17 ⋊ C2×C3
HallC2×C52×C17 ⋊ C3×C11
HallC2×C52×C11 ⋊ C3×C17
HallC52×C17 ⋊ C2×C3×C11
HallC52×C11 ⋊ C2×C3×C17
HallC2×C52 ⋊ C3×C11×C17

Subgroups

subgroupG/H
center, hypercenterC2×C11×C17C52⋊C3
commutator, cosocle, hypocenterC52C2×C3×C11×C17
FrattiniC1G
Fitting, socleC2×C52×C11×C17C3
LCSG ▷ C52
UCSC1 ◁ C2×C11×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5610

Conjugacy classes & character table

4114 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28050, 53);