Finite Group Databasebeta

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C5×D7×C23⋊C11 #31799326

order17710
automorphism?
homologyAbelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×D7×C23⋊C11
unambiguous semidirect productC7⋊(C2×C5×C23⋊C11)
unambiguous semidirect product(D7×C23)⋊(C5×C11)
unambiguous semidirect product(C5×D7×C23)⋊C11

Splittings

Fitting, socle, HallC5×C7×C23 ⋊ C2×C11
derived, HallC7×C23 ⋊ C2×C5×C11
HallC5×C7×C23⋊C11 ⋊ C2
HallC7×C23⋊C11 ⋊ C2×C5
HallC5×D7×C23 ⋊ C11
HallD7×C23 ⋊ C5×C11
HallC5×C23 ⋊ C11×D7
HallC5×C7 ⋊ C2×C23⋊C11
SylowC23 ⋊ C5×C11×D7
SylowC7 ⋊ C2×C5×C23⋊C11

Subgroups

subgroupG/H
center, hypercenterC5D7×C23⋊C11
commutator, cosocle, hypocenterC7×C23C2×C5×C11
FrattiniC1G
Fitting, socleC5×C7×C23C2×C11
LCSG ▷ C7×C23
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 805

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×D7×AGL(1,𝔽23), D7×C5⋊AGL(1,𝔽23), D5×D7×C23⋊C11, …
maximal normal subgroup ofC5×D7×AGL(1,𝔽23), D7×C5⋊AGL(1,𝔽23), D5×D7×C23⋊C11, …
maximal quotient ofC5×Dic7×C23⋊C11, C2×C5×D7×C23⋊C11

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17710, 20);