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C11×C3⋊D105 #20294208

order6930
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C3

Aliases

direct productC11×C3⋊D105
unambiguous semidirect productC3⋊(C11×D105)
unambiguous semidirect productC5⋊(C11×C3⋊D21)
unambiguous semidirect productC7⋊(C11×C3⋊D15)

Splittings

Fitting, socle, HallC32×C5×C7×C11 ⋊ C2
derived, HallC32×C5×C7 ⋊ C2×C11
HallC32×C7×C11 ⋊ D5
HallC32×C5×C11 ⋊ D7
HallC5×C7×C11 ⋊ C3⋊D3
HallC32×C11 ⋊ D35
HallC7×C11 ⋊ C3⋊D15
HallC32×C7 ⋊ D5×C11
HallC5×C11 ⋊ C3⋊D21
HallC32×C5 ⋊ C11×D7
HallC5×C7 ⋊ C11×C3⋊D3
SylowC32 ⋊ C11×D35
SylowC7 ⋊ C11×C3⋊D15
SylowC5 ⋊ C11×C3⋊D21

Subgroups

subgroupG/H
center, hypercenterC11C3⋊D105
commutator, hypocenterC32×C5×C7C2×C11
FrattiniC1G
Fitting, socleC32×C5×C7×C11C2
LCSG ▷ C32×C5×C7
UCSC1 ◁ C11

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1749 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD11×C3⋊D105, C11×D7×C3⋊D15, D77⋊(C3⋊D15), …
maximal normal subgroup ofD11×C3⋊D105, C11×D7×C3⋊D15, D77⋊(C3⋊D15), …
maximal quotient ofC11×C3⋊Dic105, C2×C11×C3⋊D105, C11×C3⋊D525, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 95);