Finite Group Databasebeta

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C2×D3×C7×C11×C25 #37528320

order23100
automorphism?
homologyAbelianization (H1) = C22×C7×C11×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×D3×C7×C11×C25
unambiguous semidirect productC3⋊(C22×C7×C11×C25)
unambiguous semidirect product(C2×C3)⋊(C2×C7×C11×C25)

Splittings

FittingC2×C3×C7×C11×C25 ⋊ C2
derived, SylowC3 ⋊ C22×C7×C11×C25
HallC3×C7×C11×C25 ⋊ C22
HallC3×C11×C25 ⋊ C22×C7
HallC3×C7×C25 ⋊ C22×C11
HallC3×C7×C11 ⋊ C22×C25
HallC3×C25 ⋊ C22×C7×C11
HallC3×C11 ⋊ C22×C7×C25
HallC3×C7 ⋊ C22×C11×C25

Subgroups

subgroupG/H
center, hypercenterC2×C7×C11×C25D3
commutator, hypocenterC3C22×C7×C11×C25
FrattiniC5C2×C5×D3×C7×C11
FittingC2×C3×C7×C11×C25C2
socleC2×C3×C5×C7×C11C2×C5
prime radicalC2×C5×D3×C7×C11C5
cosocleC3×C5C22×C5×C7×C11
LCSG ▷ C3
UCSC1 ◁ C2×C7×C11×C25

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11550

Conjugacy classes & character table

11550 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 131);