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D7×C23×C11⋊C5 #31799335

order17710
automorphism?
homologyAbelianization (H1) = C2×C5×C23 · Schur multiplier (H2) = C1

Aliases

direct productD7×C23×C11⋊C5
unambiguous semidirect productC7⋊(C2×C23×C11⋊C5)
unambiguous semidirect product(C11×D7)⋊(C5×C23)
unambiguous semidirect product(C11×D7×C23)⋊C5

Splittings

Fitting, socle, HallC7×C11×C23 ⋊ C2×C5
derived, HallC7×C11 ⋊ C2×C5×C23
HallC7×C23×C11⋊C5 ⋊ C2
HallC11×D7×C23 ⋊ C5
HallC7×C11⋊C5 ⋊ C2×C23
HallC11×C23 ⋊ C5×D7
HallC7×C23 ⋊ C2×C11⋊C5
HallC11×D7 ⋊ C5×C23
SylowC11 ⋊ C5×D7×C23
SylowC7 ⋊ C2×C23×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC23D7×C11⋊C5
commutator, cosocle, hypocenterC7×C11C2×C5×C23
FrattiniC1G
Fitting, socleC7×C11×C23C2×C5
LCSG ▷ C7×C11
UCSC1 ◁ C23

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1771

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD7×C23×AGL(1,𝔽11), D7×C23⋊AGL(1,𝔽11), D7×D23×C11⋊C5, …
maximal normal subgroup ofD7×C23×AGL(1,𝔽11), D7×C23⋊AGL(1,𝔽11), D7×D23×C11⋊C5, …
maximal quotient ofC23×Dic7×C11⋊C5, C2×D7×C23×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17710, 29);