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C7⋊(C23⋊(Dic11⋊C5)) #47978398

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

Aliases

unambiguous semidirect productC7⋊(C23⋊(Dic11⋊C5))
unambiguous semidirect productC23⋊(C7⋊(Dic11⋊C5))
unambiguous semidirect product(C11⋊C5)⋊Dic161
unambiguous semidirect productDic1771⋊C5

Splittings

derived, HallC7×C11×C23 ⋊ C4×C5
HallC7×C23×C11⋊C5 ⋊ C4
HallDic1771 ⋊ C5
HallC23×C11⋊C5 ⋊ Dic7
HallC7×C11⋊C5 ⋊ Dic23
HallC11×C23 ⋊ C5×Dic7
HallC7×C23 ⋊ Dic11⋊C5
HallC7×C11 ⋊ C5×Dic23
HallC11⋊C5 ⋊ Dic161
SylowC23 ⋊ C7⋊(Dic11⋊C5)
SylowC11 ⋊ C5×Dic161
SylowC7 ⋊ C23⋊(Dic11⋊C5)

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C7⋊(C23⋊AGL(1,𝔽11))
commutator, hypocenterC7×C11×C23C4×C5
Fitting, socle, cosocleC2×C7×C11×C23C2×C5
prime radicalC2×C7×C23×C11⋊C5C2
LCSG ▷ C7×C11×C23
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7084

Polycyclic presentation:

2,5,7,11,23,2|a^2=f,c^a=c^6,d^a=d^10,e^a=e^22,d^b=d^4

Conjugacy classes & character table

1142 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 32);