Finite Group Databasebeta

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C5×C11×D7×C31 #37558815

order23870
automorphism?
homologyAbelianization (H1) = C2×C5×C11×C31 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×D7×C31
unambiguous semidirect productC7⋊(C2×C5×C11×C31)

Splittings

Fitting, socle, HallC5×C7×C11×C31 ⋊ C2
derived, SylowC7 ⋊ C2×C5×C11×C31
HallC7×C11×C31 ⋊ C2×C5
HallC5×C7×C31 ⋊ C2×C11
HallC5×C7×C11 ⋊ C2×C31
HallC7×C31 ⋊ C2×C5×C11
HallC7×C11 ⋊ C2×C5×C31
HallC5×C7 ⋊ C2×C11×C31

Subgroups

subgroupG/H
center, hypercenterC5×C11×C31D7
commutator, cosocle, hypocenterC7C2×C5×C11×C31
FrattiniC1G
Fitting, socleC5×C7×C11×C31C2
LCSG ▷ C7
UCSC1 ◁ C5×C11×C31

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11935

Conjugacy classes & character table

8525 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23870, 11);