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D2513 #19097869

order5026
automorphismAut(G) order 5397924
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD2513
unambiguous semidirect productC7⋊D359
unambiguous semidirect productC359⋊D7

Splittings

Fitting, socle, derived, HallC7×C359 ⋊ C2
SylowC359 ⋊ D7
SylowC7 ⋊ D359

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC7×C359C2
LCSG ▷ C7×C359
UCSC1

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,7,359|b^a=b^6,c^a=c^358

Conjugacy classes & character table

1258 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×D2513, D7539, ΓL(1,𝔽8)⋊D359, …
maximal normal subgroup ofC3×D2513, ΓL(1,𝔽8)⋊D359, C5×D2513, …
maximal quotient ofC3×D2513, D7539, C5×D2513, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5026, 3);