Finite Group Databasebeta

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C5×C7⋊(Dic23⋊C11) #47978387

order35420
automorphism?
homologyAbelianization (H1) = C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7⋊(Dic23⋊C11)
unambiguous semidirect productC7⋊(C5×Dic23⋊C11)
unambiguous semidirect product(C23⋊C11)⋊(C5×Dic7)
unambiguous semidirect productDic161⋊(C5×C11)
unambiguous semidirect product(C5×Dic161)⋊C11

Splittings

derived, HallC7×C23 ⋊ C4×C5×C11
HallC5×C7×C23⋊C11 ⋊ C4
HallC5×Dic161 ⋊ C11
HallC7×C23⋊C11 ⋊ C4×C5
HallC5×C23⋊C11 ⋊ Dic7
HallC5×C7×C23 ⋊ C4×C11
HallDic161 ⋊ C5×C11
HallC23⋊C11 ⋊ C5×Dic7
HallC5×C23 ⋊ C11×Dic7
HallC5×C7 ⋊ Dic23⋊C11
SylowC23 ⋊ C5×C11×Dic7
SylowC7 ⋊ C5×Dic23⋊C11

Subgroups

subgroupG/H
center, hypercenterC2×C5C7⋊AGL(1,𝔽23)
commutator, hypocenterC7×C23C4×C5×C11
FrattiniC2C5×C7⋊AGL(1,𝔽23)
Fitting, socleC2×C5×C7×C23C2×C11
prime radicalC2×C5×C7×C23⋊C11C2
cosocleC2×C7×C23C2×C5×C11
LCSG ▷ C7×C23
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3220

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 21);