Finite Group Databasebeta

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C11×#14558785 #39911809

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

Aliases

direct productC11×#14558785

Splittings

derived, HallC7×C19 ⋊ C2×C9×C11
HallC11×#11924777 ⋊ C2
HallC11×D7×C19 ⋊ C9
HallC7×C11×C19 ⋊ C2×C9
Hall#11924777 ⋊ C2×C11
HallD7×C19 ⋊ C9×C11
HallC11×C19 ⋊ D7⋊C9
HallC11×D7 ⋊ #4294
HallC7×C11 ⋊ C2×#4294
SylowC19 ⋊ C11×D7⋊C9
HallD7 ⋊ C11×#4294
SylowC7 ⋊ C2×C11×#4294

Subgroups

subgroupG/H
center, hypercenterC3×C11#11716326
commutator, hypocenterC7×C19C2×C9×C11
FrattiniC3C11×#11716326
Fitting, socleC3×C7×C11×C19C2×C3
prime radicalC3×C11×D7×C19C3
cosocleC3×C7×C19C2×C3×C11
LCSG ▷ C7×C19
UCSC1 ◁ C3×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13167

Conjugacy classes & character table

1221 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26334, 36);