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C5×D741 #20301809

order7410
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D741
unambiguous semidirect productC3⋊(C5×D247)
unambiguous semidirect productC13⋊(C5×D57)
unambiguous semidirect productC19⋊(C5×D39)

Splittings

Fitting, socle, HallC3×C5×C13×C19 ⋊ C2
derived, HallC3×C13×C19 ⋊ C2×C5
HallC5×C13×C19 ⋊ D3
HallC3×C5×C19 ⋊ D13
HallC13×C19 ⋊ C5×D3
HallC3×C5×C13 ⋊ D19
HallC5×C19 ⋊ D39
HallC5×C13 ⋊ D57
HallC3×C19 ⋊ C5×D13
HallC3×C13 ⋊ C5×D19
SylowC19 ⋊ C5×D39
HallC3×C5 ⋊ D247
SylowC13 ⋊ C5×D57
SylowC3 ⋊ C5×D247

Subgroups

subgroupG/H
center, hypercenterC5D741
commutator, hypocenterC3×C13×C19C2×C5
FrattiniC1G
Fitting, socleC3×C5×C13×C19C2
LCSG ▷ C3×C13×C19
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1860 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D19×D39, C5×D13×D57, C5×D3×D247, …
maximal normal subgroup ofC5×D19×D39, C5×D13×D57, C5×D3×D247, …
maximal quotient ofC5×Dic741, C2×C5×D741, C5×D2223, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7410, 16);