Finite Group Databasebeta

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C11×#14558780 #39911796

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

Aliases

direct productC11×#14558780

Splittings

derived, HallC7×C19 ⋊ C2×C9×C11
HallC11×#11924776 ⋊ C2
HallC7×C11×D19 ⋊ C9
HallC7×C11×C19 ⋊ C2×C9
Hall#11924776 ⋊ C2×C11
HallC11×D19 ⋊ C7⋊C9
HallC7×D19 ⋊ C9×C11
HallC11×C19 ⋊ C2×C7⋊C9
HallC7×C11 ⋊ #4294⋊C2
HallD19 ⋊ C11×C7⋊C9
SylowC19 ⋊ C2×C11×C7⋊C9
SylowC7 ⋊ C11×#4294⋊C2

Subgroups

subgroupG/H
center, hypercenterC3×C11#11716321
commutator, hypocenterC7×C19C2×C9×C11
FrattiniC3C11×#11716321
Fitting, socleC3×C7×C11×C19C2×C3
prime radicalC3×C7×C11×D19C3
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

1023 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26334, 23);