Finite Group Databasebeta

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C11×C49×C11⋊C5 #44445684

order29645
automorphism?
homologyAbelianization (H1) = C5×C11×C49 · Schur multiplier (H2) = C1

Aliases

direct productC11×C49×C11⋊C5
unambiguous semidirect productC11⋊(C5×C11×C49)
unambiguous semidirect product(C11×C49)⋊(C5×C11)

Splittings

Fitting, HallC112×C49 ⋊ C5
derivedC11 ⋊ C5×C11×C49
SylowC112 ⋊ C5×C49

Subgroups

subgroupG/H
center, hypercenterC11×C49C11⋊C5
commutator, hypocenterC11C5×C11×C49
FrattiniC7C7×C11×C11⋊C5
FittingC112×C49C5
socleC7×C112C5×C7
prime radicalC7×C11×C11⋊C5C7
cosocleC7×C11C5×C7×C11
LCSG ▷ C11
UCSC1 ◁ C11×C49

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2695

Conjugacy classes & character table

3773 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29645, 7);