Finite Group Databasebeta

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C3×C17×(C5⋊D5)⋊D7 #49087896

order35700
automorphism?
homologyAbelianization (H1) = C22×C3×C17 · Schur multiplier (H2) = C2

Aliases

direct productC3×C17×(C5⋊D5)⋊D7

Splittings

Fitting, socle, HallC3×C52×C7×C17 ⋊ C22
derived, HallC52×C7 ⋊ C22×C3×C17
HallC52×C7×C17 ⋊ C22×C3
HallC3×C52×C17 ⋊ C2×D7
HallC3×C52×C7 ⋊ C22×C17
HallC52×C17 ⋊ C2×C3×D7
HallC3×C7×C17 ⋊ D52
HallC7×C17 ⋊ C3×D52
HallC3×C52 ⋊ C2×D7×C17
SylowC52 ⋊ C2×C3×D7×C17
HallC3×C7 ⋊ D52×C17
SylowC7 ⋊ C3×D52×C17

Subgroups

subgroupG/H
center, hypercenterC3×C17(C5⋊D5)⋊D7
commutator, cosocle, hypocenterC52×C7C22×C3×C17
FrattiniC1G
Fitting, socleC3×C52×C7×C17C22
LCSG ▷ C52×C7
UCSC1 ◁ C3×C17

192 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 60 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

2958 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35700, 370);