Finite Group Databasebeta

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C7×C23×Dic11⋊C5 #47978393

order35420
automorphism?
homologyAbelianization (H1) = C4×C5×C7×C23 · Schur multiplier (H2) = C1

Aliases

direct productC7×C23×Dic11⋊C5
unambiguous semidirect productDic11⋊(C5×C7×C23)
unambiguous semidirect product(C11⋊C5)⋊(C4×C7×C23)
unambiguous semidirect product(C7×Dic11)⋊(C5×C23)
unambiguous semidirect product(C23×Dic11)⋊(C5×C7)
unambiguous semidirect product(C7×C23×Dic11)⋊C5

Splittings

derived, SylowC11 ⋊ C4×C5×C7×C23
HallC7×C23×C11⋊C5 ⋊ C4
HallC7×C23×Dic11 ⋊ C5
HallC7×C11×C23 ⋊ C4×C5
HallC23×C11⋊C5 ⋊ C4×C7
HallC23×Dic11 ⋊ C5×C7
HallC7×C11⋊C5 ⋊ C4×C23
HallC7×Dic11 ⋊ C5×C23
HallC11×C23 ⋊ C4×C5×C7
HallC7×C11 ⋊ C4×C5×C23
HallC11⋊C5 ⋊ C4×C7×C23
HallDic11 ⋊ C5×C7×C23

Subgroups

subgroupG/H
center, hypercenterC2×C7×C23AGL(1,𝔽11)
commutator, hypocenterC11C4×C5×C7×C23
FrattiniC2C7×C23×AGL(1,𝔽11)
Fitting, socleC2×C7×C11×C23C2×C5
prime radicalC2×C7×C23×C11⋊C5C2
cosocleC2×C11C2×C5×C7×C23
LCSG ▷ C11
UCSC1 ◁ C2×C7×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7084

Conjugacy classes & character table

3542 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 27);