Finite Group Databasebeta

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C3×C52×D187 #43242531

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

Aliases

direct productC3×C52×D187
unambiguous semidirect productC17⋊(C3×C52×D11)

Splittings

Fitting, socle, HallC3×C52×C11×C17 ⋊ C2
derived, HallC11×C17 ⋊ C2×C3×C52
HallC52×C11×C17 ⋊ C2×C3
HallC3×C52×C17 ⋊ D11
HallC3×C52×C11 ⋊ D17
HallC3×C11×C17 ⋊ C2×C52
HallC52×C17 ⋊ C3×D11
HallC52×C11 ⋊ C3×D17
HallC3×C17 ⋊ C52×D11
HallC3×C11 ⋊ C52×D17
SylowC17 ⋊ C3×C52×D11
SylowC11 ⋊ C3×C52×D17

Subgroups

subgroupG/H
center, hypercenterC3×C52D187
commutator, cosocle, hypocenterC11×C17C2×C3×C52
FrattiniC1G
Fitting, socleC3×C52×C11×C17C2
LCSG ▷ C11×C17
UCSC1 ◁ C3×C52

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14025

Conjugacy classes & character table

7125 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28050, 56);