Finite Group Databasebeta

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C2×C7×C3⋊(D11⋊C25) #37528255

order23100
automorphism?
homologyAbelianization (H1) = C22×C7×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×C3⋊(D11⋊C25)
unambiguous semidirect product(C2×C3)⋊(C7×D11⋊C25)
unambiguous semidirect product(C2×D33)⋊(C7×C25)
unambiguous semidirect product(C2×C11⋊C25)⋊(D3×C7)
unambiguous semidirect product(C2×C7×D33)⋊C25

Splittings

derived, HallC3×C11 ⋊ C22×C7×C25
HallC3×C7×C11⋊C25 ⋊ C22
HallC7×C11⋊C25 ⋊ C2×D3
HallC2×C7×D33 ⋊ C25
HallC3×C11⋊C25 ⋊ C22×C7
HallC11⋊C25 ⋊ C2×D3×C7
HallC3×C7×C11 ⋊ C22×C25
HallC2×D33 ⋊ C7×C25
HallC7×C11 ⋊ C2×D3×C25
HallC3×C7 ⋊ C2×D11⋊C25
SylowC11 ⋊ C2×D3×C7×C25
SylowC3 ⋊ C2×C7×D11⋊C25

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7C3⋊AGL(1,𝔽11)
commutator, hypocenterC3×C11C22×C7×C25
FrattiniC5C2×C7×C3⋊AGL(1,𝔽11)
Fitting, socleC2×C3×C5×C7×C11C2×C5
prime radicalC2×C5×C7×D33C5
cosocleC3×C5×C11C22×C5×C7
LCSG ▷ C3×C11
UCSC1 ◁ C2×C5×C7

120 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 58 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) = 11550

Conjugacy classes & character table

1260 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 66);