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C5×D2737 #41032844

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

Aliases

direct productC5×D2737
unambiguous semidirect productC7⋊(C5×D391)
unambiguous semidirect productC17⋊(C5×D161)
unambiguous semidirect productC23⋊(C5×D119)

Splittings

Fitting, socle, HallC5×C7×C17×C23 ⋊ C2
derived, HallC7×C17×C23 ⋊ C2×C5
HallC5×C17×C23 ⋊ D7
HallC5×C7×C23 ⋊ D17
HallC5×C7×C17 ⋊ D23
HallC17×C23 ⋊ C5×D7
HallC7×C23 ⋊ C5×D17
HallC7×C17 ⋊ C5×D23
HallC5×C23 ⋊ D119
HallC5×C17 ⋊ D161
HallC5×C7 ⋊ D391
SylowC23 ⋊ C5×D119
SylowC17 ⋊ C5×D161
SylowC7 ⋊ C5×D391

Subgroups

subgroupG/H
center, hypercenterC5D2737
commutator, cosocle, hypocenterC7×C17×C23C2×C5
FrattiniC1G
Fitting, socleC5×C7×C17×C23C2
LCSG ▷ C7×C17×C23
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13685

Conjugacy classes & character table

6850 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27370, 8);