Finite Group Databasebeta

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C5×D2387 #37558818

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

Aliases

direct productC5×D2387
unambiguous semidirect productC7⋊(C5×D341)

Splittings

Fitting, socle, HallC5×C7×C11×C31 ⋊ C2
derived, HallC7×C11×C31 ⋊ C2×C5
HallC5×C11×C31 ⋊ D7
HallC5×C7×C31 ⋊ D11
HallC5×C7×C11 ⋊ D31
HallC11×C31 ⋊ C5×D7
HallC7×C31 ⋊ C5×D11
HallC5×C31 ⋊ D77
HallC7×C11 ⋊ C5×D31
HallC5×C11 ⋊ D217
HallC5×C7 ⋊ D341
SylowC31 ⋊ C5×D77
SylowC11 ⋊ C5×D217
SylowC7 ⋊ C5×D341

Subgroups

subgroupG/H
center, hypercenterC5D2387
commutator, cosocle, hypocenterC7×C11×C31C2×C5
FrattiniC1G
Fitting, socleC5×C7×C11×C31C2
LCSG ▷ C7×C11×C31
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11935

Conjugacy classes & character table

5975 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23870, 14);