Finite Group Databasebeta

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C11×C3⋊D357 #37555668

order23562
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C3

Aliases

direct productC11×C3⋊D357
unambiguous semidirect productC3⋊(C11×D357)
unambiguous semidirect productC7⋊(C11×C3⋊D51)
unambiguous semidirect productC17⋊(C11×C3⋊D21)

Splittings

Fitting, socle, HallC32×C7×C11×C17 ⋊ C2
derived, HallC32×C7×C17 ⋊ C2×C11
HallC32×C11×C17 ⋊ D7
HallC7×C11×C17 ⋊ C3⋊D3
HallC32×C7×C11 ⋊ D17
HallC11×C17 ⋊ C3⋊D21
HallC32×C17 ⋊ C11×D7
HallC7×C17 ⋊ C11×C3⋊D3
HallC32×C11 ⋊ D119
HallC7×C11 ⋊ C3⋊D51
HallC32×C7 ⋊ C11×D17
SylowC17 ⋊ C11×C3⋊D21
SylowC32 ⋊ C11×D119
SylowC7 ⋊ C11×C3⋊D51

Subgroups

subgroupG/H
center, hypercenterC11C3⋊D357
commutator, cosocle, hypocenterC32×C7×C17C2×C11
FrattiniC1G
Fitting, socleC32×C7×C11×C17C2
LCSG ▷ C32×C7×C17
UCSC1 ◁ C11

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11781

Conjugacy classes & character table

5907 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23562, 62);