Finite Group Databasebeta

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C5×C7×D391 #41032840

order27370
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×D391
unambiguous semidirect productC17⋊(C5×C7×D23)
unambiguous semidirect productC23⋊(C5×C7×D17)

Splittings

Fitting, socle, HallC5×C7×C17×C23 ⋊ C2
derived, HallC17×C23 ⋊ C2×C5×C7
HallC7×C17×C23 ⋊ C2×C5
HallC5×C17×C23 ⋊ C2×C7
HallC5×C7×C23 ⋊ D17
HallC5×C7×C17 ⋊ D23
HallC7×C23 ⋊ C5×D17
HallC7×C17 ⋊ C5×D23
HallC5×C23 ⋊ C7×D17
HallC5×C17 ⋊ C7×D23
SylowC23 ⋊ C5×C7×D17
SylowC17 ⋊ C5×C7×D23

Subgroups

subgroupG/H
center, hypercenterC5×C7D391
commutator, cosocle, hypocenterC17×C23C2×C5×C7
FrattiniC1G
Fitting, socleC5×C7×C17×C23C2
LCSG ▷ C17×C23
UCSC1 ◁ C5×C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13685

Conjugacy classes & character table

6895 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27370, 4);