Finite Group Databasebeta

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C2×C7⋊C9×C11⋊C25 #46831361

order34650
automorphism?
homologyAbelianization (H1) = C2×C9×C25 · Schur multiplier (H2) = C1

Aliases

direct productC2×C7⋊C9×C11⋊C25
unambiguous semidirect product(C2×C7)⋊(C9×C11⋊C25)
unambiguous semidirect product(C2×C11)⋊(C25×C7⋊C9)
unambiguous semidirect product(C2×C11×C7⋊C9)⋊C25
unambiguous semidirect product(C2×C7×C11⋊C25)⋊C9

Splittings

derived, HallC7×C11 ⋊ C2×C9×C25
HallC2×C7×C11⋊C25 ⋊ C9
HallC7×C11⋊C25 ⋊ C2×C9
HallC2×C11×C7⋊C9 ⋊ C25
HallC11×C7⋊C9 ⋊ C2×C25
HallC2×C7×C11 ⋊ C9×C25
HallC2×C11 ⋊ C25×C7⋊C9
HallC2×C7 ⋊ C9×C11⋊C25
SylowC11 ⋊ C2×C25×C7⋊C9
SylowC7 ⋊ C2×C9×C11⋊C25

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5ΓL(1,𝔽8)×C11⋊C5
commutator, hypocenterC7×C11C2×C9×C25
FrattiniC3×C5C2×ΓL(1,𝔽8)×C11⋊C5
Fitting, socle, prime radicalC2×C3×C5×C7×C11C3×C5
cosocleC3×C5×C7×C11C2×C3×C5
LCSG ▷ C7×C11
UCSC1 ◁ C2×C3×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 34650

Conjugacy classes & character table

1050 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 4);