Finite Group Databasebeta

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C3×D11×D175 #37528273

order23100
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×D11×D175
unambiguous semidirect product(D11×C25)⋊(C3×D7)

Splittings

Fitting, HallC3×C7×C11×C25 ⋊ C22
derived, HallC7×C11×C25 ⋊ C22×C3
HallC3×C11×C25 ⋊ C2×D7
HallC3×C7×C25 ⋊ C2×D11
HallC11×C25 ⋊ C2×C3×D7
HallC3×C7×C11 ⋊ C2×D25
HallC7×C25 ⋊ C2×C3×D11
HallC7×C11 ⋊ C2×C3×D25
HallC3×C25 ⋊ D7×D11
HallC3×C11 ⋊ C2×D175
SylowC25 ⋊ C3×D7×D11
HallC3×C7 ⋊ D11×D25
SylowC11 ⋊ C2×C3×D175
SylowC7 ⋊ C3×D11×D25

Subgroups

subgroupG/H
center, hypercenterC3D11×D175
commutator, cosocle, hypocenterC7×C11×C25C22×C3
FrattiniC5C3×D11×D35
FittingC3×C7×C11×C25C22
socleC3×C5×C7×C11C2×D5
LCSG ▷ C7×C11×C25
UCSC1 ◁ C3

120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 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) = 5775

Conjugacy classes & character table

1869 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 84);