Finite Group Databasebeta

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C31×D385 #37558825

order23870
automorphism?
homologyAbelianization (H1) = C2×C31 · Schur multiplier (H2) = C1

Aliases

direct productC31×D385
unambiguous semidirect productC5⋊(C31×D77)
unambiguous semidirect productC7⋊(C31×D55)
unambiguous semidirect productC11⋊(C31×D35)

Splittings

Fitting, socle, HallC5×C7×C11×C31 ⋊ C2
derived, HallC5×C7×C11 ⋊ C2×C31
HallC7×C11×C31 ⋊ D5
HallC5×C11×C31 ⋊ D7
HallC5×C7×C31 ⋊ D11
HallC11×C31 ⋊ D35
HallC7×C31 ⋊ D55
HallC5×C31 ⋊ D77
HallC7×C11 ⋊ D5×C31
HallC5×C11 ⋊ D7×C31
HallC5×C7 ⋊ D11×C31
SylowC11 ⋊ C31×D35
SylowC7 ⋊ C31×D55
SylowC5 ⋊ C31×D77

Subgroups

subgroupG/H
center, hypercenterC31D385
commutator, cosocle, hypocenterC5×C7×C11C2×C31
FrattiniC1G
Fitting, socleC5×C7×C11×C31C2
LCSG ▷ C5×C7×C11
UCSC1 ◁ C31

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11935

Conjugacy classes & character table

6014 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23870, 21);