Finite Group Databasebeta

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C5×D5×D357 #49087942

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

Aliases

direct productC5×D5×D357
unambiguous semidirect product(C3×D5)⋊(C5×D119)
unambiguous semidirect product(C7×D5)⋊(C5×D51)
unambiguous semidirect product(D5×C17)⋊(C5×D21)

Splittings

Fitting, socle, HallC3×C52×C7×C17 ⋊ C22
derivedC3×C5×C7×C17 ⋊ C22×C5
HallC52×C7×C17 ⋊ C2×D3
HallC3×C52×C17 ⋊ C2×D7
HallC3×C52×C7 ⋊ C2×D17
HallC52×C17 ⋊ C2×D21
HallC3×C7×C17 ⋊ C2×C5×D5
HallC52×C7 ⋊ C2×D51
HallC7×C17 ⋊ C5×D3×D5
HallC3×C52 ⋊ C2×D119
HallC3×C17 ⋊ C5×D5×D7
SylowC52 ⋊ C2×D357
HallC3×C7 ⋊ C5×D5×D17
SylowC17 ⋊ C5×D5×D21
SylowC7 ⋊ C5×D5×D51
SylowC3 ⋊ C5×D5×D119

Subgroups

subgroupG/H
center, hypercenterC5D5×D357
commutator, cosocle, hypocenterC3×C5×C7×C17C22×C5
FrattiniC1G
Fitting, socleC3×C52×C7×C17C22
LCSG ▷ C3×C5×C7×C17
UCSC1 ◁ C5

192 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 56 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) = 3570

Conjugacy classes & character table

3600 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35700, 416);