Finite Group Databasebeta

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C7×D1705 #37558822

order23870
automorphism?
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D1705
unambiguous semidirect productC5⋊(C7×D341)
unambiguous semidirect productC11⋊(C7×D155)
unambiguous semidirect productC31⋊(C7×D55)

Splittings

Fitting, socle, HallC5×C7×C11×C31 ⋊ C2
derived, HallC5×C11×C31 ⋊ C2×C7
HallC7×C11×C31 ⋊ D5
HallC5×C7×C31 ⋊ D11
HallC5×C7×C11 ⋊ D31
HallC11×C31 ⋊ C7×D5
HallC7×C31 ⋊ D55
HallC5×C31 ⋊ C7×D11
HallC7×C11 ⋊ D155
HallC5×C11 ⋊ C7×D31
HallC5×C7 ⋊ D341
SylowC31 ⋊ C7×D55
SylowC11 ⋊ C7×D155
SylowC5 ⋊ C7×D341

Subgroups

subgroupG/H
center, hypercenterC7D1705
commutator, cosocle, hypocenterC5×C11×C31C2×C7
FrattiniC1G
Fitting, socleC5×C7×C11×C31C2
LCSG ▷ C5×C11×C31
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11935

Conjugacy classes & character table

5978 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23870, 18);