Finite Group Databasebeta

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D3×C5⋊D595 #49088013

order35700
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2×C5

Aliases

direct productD3×C5⋊D595
unambiguous semidirect product(C5×D3)⋊D595
unambiguous semidirect product(D3×C7)⋊(C5⋊D85)
unambiguous semidirect product(D3×C17)⋊(C5⋊D35)

Splittings

Fitting, socle, derived, HallC3×C52×C7×C17 ⋊ C22
HallC52×C7×C17 ⋊ C2×D3
HallC3×C52×C17 ⋊ C2×D7
HallC3×C52×C7 ⋊ C2×D17
HallC52×C17 ⋊ D3×D7
HallC3×C7×C17 ⋊ C2×C5⋊D5
HallC52×C7 ⋊ D3×D17
HallC7×C17 ⋊ D3×C5⋊D5
HallC3×C52 ⋊ C2×D119
HallC3×C17 ⋊ C2×C5⋊D35
SylowC52 ⋊ D3×D119
HallC3×C7 ⋊ C2×C5⋊D85
SylowC17 ⋊ D3×C5⋊D35
SylowC7 ⋊ D3×C5⋊D85
SylowC3 ⋊ C2×C5⋊D595

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C52×C7×C17C22
LCSG ▷ C3×C52×C7×C17
UCSC1

320 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8925

Conjugacy classes & character table

4467 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35700, 487);