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C17×(C31⋊C3)⋊D7 #36349012

order22134
automorphism?
homologyAbelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×(C31⋊C3)⋊D7
unambiguous semidirect product(C31⋊C3)⋊(D7×C17)

Splittings

Fitting, socle, HallC7×C17×C31 ⋊ C2×C3
derived, HallC7×C31 ⋊ C2×C3×C17
HallC7×C17×C31⋊C3 ⋊ C2
HallC17×D217 ⋊ C3
HallC17×C31⋊C3 ⋊ D7
HallC7×C31⋊C3 ⋊ C2×C17
HallC17×C31 ⋊ C3×D7
HallD217 ⋊ C3×C17
HallC7×C17 ⋊ D31⋊C3
HallC31⋊C3 ⋊ D7×C17
SylowC31 ⋊ C3×D7×C17
SylowC7 ⋊ C17×D31⋊C3

Subgroups

subgroupG/H
center, hypercenterC17(C31⋊C3)⋊D7
commutator, cosocle, hypocenterC7×C31C2×C3×C17
FrattiniC1G
Fitting, socleC7×C17×C31C2×C3
LCSG ▷ C7×C31
UCSC1 ◁ C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3689

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22134, 37);