Finite Group Databasebeta

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C11×C7⋊(D29⋊C7) #44530501

order31262
automorphism?
homologyAbelianization (H1) = C2×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C7⋊(D29⋊C7)
unambiguous semidirect productC7⋊(C11×D29⋊C7)
unambiguous semidirect product(C29⋊C7)⋊(C11×D7)
unambiguous semidirect productD203⋊(C7×C11)
unambiguous semidirect product(C11×D203)⋊C7

Splittings

Fitting, socleC7×C11×C29 ⋊ C2×C7
derivedC7×C29 ⋊ C2×C7×C11
HallC7×C11×C29⋊C7 ⋊ C2
HallC7×C29⋊C7 ⋊ C2×C11
HallC11×C29 ⋊ C7×D7
SylowC29 ⋊ C7×C11×D7

Subgroups

subgroupG/H
center, hypercenterC11C7⋊(D29⋊C7)
commutator, cosocle, hypocenterC7×C29C2×C7×C11
FrattiniC1G
Fitting, socleC7×C11×C29C2×C7
LCSG ▷ C7×C29
UCSC1 ◁ C11

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2233

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31262, 17);