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C7×D5×C23⋊C11 #31799328

order17710
automorphism?
homologyAbelianization (H1) = C2×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC7×D5×C23⋊C11
unambiguous semidirect productC5⋊(C2×C7×C23⋊C11)
unambiguous semidirect product(D5×C23)⋊(C7×C11)
unambiguous semidirect product(C7×D5×C23)⋊C11

Splittings

Fitting, socle, HallC5×C7×C23 ⋊ C2×C11
derived, HallC5×C23 ⋊ C2×C7×C11
HallC5×C7×C23⋊C11 ⋊ C2
HallC7×D5×C23 ⋊ C11
HallC5×C23⋊C11 ⋊ C2×C7
HallD5×C23 ⋊ C7×C11
HallC7×C23 ⋊ D5×C11
HallC5×C7 ⋊ C2×C23⋊C11
SylowC23 ⋊ C7×D5×C11
SylowC5 ⋊ C2×C7×C23⋊C11

Subgroups

subgroupG/H
center, hypercenterC7D5×C23⋊C11
commutator, cosocle, hypocenterC5×C23C2×C7×C11
FrattiniC1G
Fitting, socleC5×C7×C23C2×C11
LCSG ▷ C5×C23
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 805

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC7×(C23⋊C11)⋊AGL(1,𝔽5), C7×AGL(1,𝔽5)×C23⋊C11, C7⋊((C23⋊C11)⋊AGL(1,𝔽5)), …
maximal normal subgroup ofC7×(C23⋊C11)⋊AGL(1,𝔽5), C7×AGL(1,𝔽5)×C23⋊C11, C7⋊((C23⋊C11)⋊AGL(1,𝔽5)), …
maximal quotient ofC7×Dic5×C23⋊C11, C2×C7×D5×C23⋊C11

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17710, 22);