Finite Group Databasebeta

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C52⋊C3×D187 #43242518

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

Aliases

direct productC52⋊C3×D187
unambiguous semidirect productC11⋊(D17×C52⋊C3)
unambiguous semidirect productC17⋊(D11×C52⋊C3)
unambiguous semidirect product(C52×D187)⋊C3

Splittings

Fitting, socle, derived, HallC52×C11×C17 ⋊ C2×C3
HallC11×C17×C52⋊C3 ⋊ C2
HallC52×D187 ⋊ C3
HallC17×C52⋊C3 ⋊ D11
HallC11×C52⋊C3 ⋊ D17
HallC52×C17 ⋊ C3×D11
HallC52×C11 ⋊ C3×D17
HallC11×C17 ⋊ C2×C52⋊C3
SylowC52 ⋊ C3×D187
SylowC17 ⋊ D11×C52⋊C3
SylowC11 ⋊ D17×C52⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C11×C17C2×C3
LCSG ▷ C52×C11×C17
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2805

Conjugacy classes & character table

1045 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28050, 43);