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D2555 #19103914

order5110
automorphismAut(G) order 4415040
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD2555
unambiguous semidirect productC5⋊D511
unambiguous semidirect productC7⋊D365
unambiguous semidirect productC73⋊D35

Splittings

Fitting, socle, derived, HallC5×C7×C73 ⋊ C2
HallC7×C73 ⋊ D5
HallC5×C73 ⋊ D7
SylowC73 ⋊ D35
HallC5×C7 ⋊ D73
SylowC7 ⋊ D365
SylowC5 ⋊ D511

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C7×C73C2
LCSG ▷ C5×C7×C73
UCSC1

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,5,7,73|b^a=b^4,c^a=c^6,d^a=d^72

Conjugacy classes & character table

1279 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×D2555, D7665, C5⋊((C73⋊C3)⋊D7), …
maximal normal subgroup ofC3×D2555, C5⋊((C73⋊C3)⋊D7), C5⋊(ΓL(1,𝔽8)⋊D73), …
maximal quotient ofC3×D2555, D7665, D12775, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5110, 8);