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C2×C11×#11924781 #39911853

order26334
automorphism?
homologyAbelianization (H1) = C2×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC2×C11×#11924781

Splittings

Fitting, socle, HallC2×C7×C11×C19 ⋊ C9
derived, HallC7×C19 ⋊ C2×C9×C11
HallC7×C11×C19 ⋊ C2×C9
HallC2×C11×C19 ⋊ C7⋊C9
HallC2×C7×C19 ⋊ C9×C11
HallC11×C19 ⋊ C2×C7⋊C9
HallC2×C7×C11 ⋊ #4296
HallC7×C11 ⋊ C2×#4296
HallC2×C19 ⋊ C11×C7⋊C9
SylowC19 ⋊ C2×C11×C7⋊C9
HallC2×C7 ⋊ C11×#4296
SylowC7 ⋊ C2×C11×#4296

Subgroups

subgroupG/H
center, hypercenterC2×C11#11924781
commutator, hypocenterC7×C19C2×C9×C11
FrattiniC1G
Fitting, socleC2×C7×C11×C19C9
prime radicalC2×C7×C11×C19⋊C3C3
cosocleC7×C19⋊C3C2×C3×C11
LCSG ▷ C7×C19
UCSC1 ◁ C2×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2926

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26334, 80);