Finite Group Databasebeta

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C11×D1085 #37558824

order23870
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×D1085
unambiguous semidirect productC5⋊(C11×D217)
unambiguous semidirect productC7⋊(C11×D155)
unambiguous semidirect productC31⋊(C11×D35)

Splittings

Fitting, socle, HallC5×C7×C11×C31 ⋊ C2
derived, HallC5×C7×C31 ⋊ C2×C11
HallC7×C11×C31 ⋊ D5
HallC5×C11×C31 ⋊ D7
HallC5×C7×C11 ⋊ D31
HallC11×C31 ⋊ D35
HallC7×C31 ⋊ D5×C11
HallC5×C31 ⋊ C11×D7
HallC7×C11 ⋊ D155
HallC5×C11 ⋊ D217
HallC5×C7 ⋊ C11×D31
SylowC31 ⋊ C11×D35
SylowC7 ⋊ C11×D155
SylowC5 ⋊ C11×D217

Subgroups

subgroupG/H
center, hypercenterC11D1085
commutator, cosocle, hypocenterC5×C7×C31C2×C11
FrattiniC1G
Fitting, socleC5×C7×C11×C31C2
LCSG ▷ C5×C7×C31
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11935

Conjugacy classes & character table

5984 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23870, 20);