Finite Group Databasebeta

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C3×C52×C11×D17 #43242529

order28050
automorphism?
homologyAbelianization (H1) = C2×C3×C52×C11 · Schur multiplier (H2) = C5

Aliases

direct productC3×C52×C11×D17
unambiguous semidirect productC17⋊(C2×C3×C52×C11)

Splittings

Fitting, socle, HallC3×C52×C11×C17 ⋊ C2
derived, SylowC17 ⋊ C2×C3×C52×C11
HallC52×C11×C17 ⋊ C2×C3
HallC3×C52×C17 ⋊ C2×C11
HallC3×C11×C17 ⋊ C2×C52
HallC52×C17 ⋊ C2×C3×C11
HallC11×C17 ⋊ C2×C3×C52
HallC3×C17 ⋊ C2×C52×C11

Subgroups

subgroupG/H
center, hypercenterC3×C52×C11D17
commutator, cosocle, hypocenterC17C2×C3×C52×C11
FrattiniC1G
Fitting, socleC3×C52×C11×C17C2
LCSG ▷ C17
UCSC1 ◁ C3×C52×C11

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14025

Conjugacy classes & character table

8250 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28050, 54);