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C7⋊AGL(1,𝔽5)×C23⋊C11 #47978404

order35420
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC7⋊AGL(1,𝔽5)×C23⋊C11
unambiguous semidirect productC7⋊(AGL(1,𝔽5)×C23⋊C11)
unambiguous semidirect product(C23×C7⋊AGL(1,𝔽5))⋊C11

Splittings

Fitting, socle, derived, HallC5×C7×C23 ⋊ C4×C11
HallC5×C7×C23⋊C11 ⋊ C4
HallC23×C7⋊AGL(1,𝔽5) ⋊ C11
HallC7×C23⋊C11 ⋊ AGL(1,𝔽5)
HallC5×C23⋊C11 ⋊ Dic7
HallC7×C23 ⋊ C11×AGL(1,𝔽5)
HallC5×C23 ⋊ C11×Dic7
HallC5×C7 ⋊ C4×C23⋊C11
SylowC23 ⋊ C11×C7⋊AGL(1,𝔽5)
SylowC7 ⋊ AGL(1,𝔽5)×C23⋊C11
SylowC5 ⋊ Dic7×C23⋊C11

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C7×C23C4×C11
prime radicalC7×D5×C23⋊C11C2
cosocleC7×D5×C23C2×C11
LCSG ▷ C5×C7×C23
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 805

Conjugacy classes & character table

221 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 38);