Finite Group Databasebeta

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C2×C7×C25×C7⋊C9 #36347644

order22050
automorphism?
homologyAbelianization (H1) = C2×C7×C9×C25 · Schur multiplier (H2) = C1

Aliases

direct productC2×C7×C25×C7⋊C9
unambiguous semidirect product(C2×C7)⋊(C7×C9×C25)
unambiguous semidirect product(C2×C7×C25)⋊(C7×C9)

Splittings

derivedC7 ⋊ C2×C7×C9×C25
HallC2×C72×C25 ⋊ C9
HallC72×C25 ⋊ C2×C9
HallC2×C72 ⋊ C9×C25
SylowC72 ⋊ C2×C9×C25

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7×C25ΓL(1,𝔽8)
commutator, hypocenterC7C2×C7×C9×C25
FrattiniC3×C5C2×C5×C7×ΓL(1,𝔽8)
FittingC2×C3×C72×C25C3
socle, prime radicalC2×C3×C5×C72C3×C5
cosocleC3×C5×C7C2×C3×C5×C7
LCSG ▷ C7
UCSC1 ◁ C2×C3×C7×C25

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3150

Conjugacy classes & character table

5250 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22050, 81);