Finite Group Databasebeta

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C3×D7×D11⋊C25 #37528231

order23100
automorphism?
homologyAbelianization (H1) = C22×C3×C25 · Schur multiplier (H2) = C2

Aliases

direct productC3×D7×D11⋊C25
unambiguous semidirect productD11⋊(C3×D7×C25)
unambiguous semidirect product(C3×D7×D11)⋊C25

Splittings

derived, HallC7×C11 ⋊ C22×C3×C25
HallC3×C7×C11⋊C25 ⋊ C22
HallC7×C11⋊C25 ⋊ C22×C3
HallC3×D7×D11 ⋊ C25
HallC3×C11⋊C25 ⋊ C2×D7
HallD7×D11 ⋊ C3×C25
HallC11⋊C25 ⋊ C2×C3×D7
HallC3×C7×C11 ⋊ C22×C25
HallC3×C11 ⋊ C2×D7×C25
HallC3×C7 ⋊ C2×D11⋊C25
SylowC11 ⋊ C2×C3×D7×C25
SylowC7 ⋊ C2×C3×D11⋊C25

Subgroups

subgroupG/H
center, hypercenterC3×C5D7×AGL(1,𝔽11)
commutator, hypocenterC7×C11C22×C3×C25
FrattiniC5C3×D7×AGL(1,𝔽11)
Fitting, socleC3×C5×C7×C11C22×C5
prime radicalC3×C5×D7×D11C5
cosocleC5×C7×C11C22×C3×C5
LCSG ▷ C7×C11
UCSC1 ◁ C3×C5

120 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 54 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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 42);