Finite Group Databasebeta

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C11⋊C5×Dic161 #47978396

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

Aliases

direct productC11⋊C5×Dic161
unambiguous semidirect productC7⋊(C11⋊C5×Dic23)
unambiguous semidirect productC23⋊(Dic7×C11⋊C5)
unambiguous semidirect product(C11×Dic161)⋊C5

Splittings

derived, HallC7×C11×C23 ⋊ C4×C5
HallC7×C23×C11⋊C5 ⋊ C4
HallC11×Dic161 ⋊ C5
HallC23×C11⋊C5 ⋊ Dic7
HallC7×C11⋊C5 ⋊ Dic23
HallC11×C23 ⋊ C5×Dic7
HallC7×C23 ⋊ C4×C11⋊C5
HallC7×C11 ⋊ C5×Dic23
SylowC23 ⋊ Dic7×C11⋊C5
SylowC11 ⋊ C5×Dic161
SylowC7 ⋊ C11⋊C5×Dic23

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C11⋊C5×D161
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

Conjugacy classes & character table

1148 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 30);