Finite Group Databasebeta

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C2×C3×C7×D275 #37528317

order23100
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C7×D275
unambiguous semidirect product(C2×C11)⋊(C3×C7×D25)
unambiguous semidirect product(C2×C25)⋊(C3×C7×D11)

Splittings

FittingC2×C3×C7×C11×C25 ⋊ C2
derived, HallC11×C25 ⋊ C22×C3×C7
HallC3×C7×C11×C25 ⋊ C22
HallC7×C11×C25 ⋊ C22×C3
HallC3×C11×C25 ⋊ C22×C7
HallC3×C7×C25 ⋊ C2×D11
HallC3×C7×C11 ⋊ C2×D25
HallC7×C25 ⋊ C2×C3×D11
HallC7×C11 ⋊ C2×C3×D25
HallC3×C25 ⋊ C2×C7×D11
HallC3×C11 ⋊ C2×C7×D25
SylowC25 ⋊ C2×C3×C7×D11
SylowC11 ⋊ C2×C3×C7×D25

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7D275
commutator, cosocle, hypocenterC11×C25C22×C3×C7
FrattiniC5C2×C3×C7×D55
FittingC2×C3×C7×C11×C25C2
socleC2×C3×C5×C7×C11D5
LCSG ▷ C11×C25
UCSC1 ◁ C2×C3×C7

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11550

Conjugacy classes & character table

5838 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 128);