Finite Group Databasebeta

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D5×C11×C67⋊C3 #36348643

order22110
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productD5×C11×C67⋊C3
unambiguous semidirect productC5⋊(C2×C11×C67⋊C3)
unambiguous semidirect product(D5×C11×C67)⋊C3

Splittings

Fitting, socle, HallC5×C11×C67 ⋊ C2×C3
derived, HallC5×C67 ⋊ C2×C3×C11
HallC5×C11×C67⋊C3 ⋊ C2
HallD5×C11×C67 ⋊ C3
HallC5×C67⋊C3 ⋊ C2×C11
HallC11×C67 ⋊ C3×D5
HallD5×C67 ⋊ C3×C11
SylowC67 ⋊ C3×D5×C11
HallC5×C11 ⋊ C2×C67⋊C3
SylowC5 ⋊ C2×C11×C67⋊C3

Subgroups

subgroupG/H
center, hypercenterC11D5×C67⋊C3
commutator, cosocle, hypocenterC5×C67C2×C3×C11
FrattiniC1G
Fitting, socleC5×C11×C67C2×C3
LCSG ▷ C5×C67
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3685

Conjugacy classes & character table

1100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22110, 39);