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C2×D1309 #19104992

order5236
automorphismAut(G) order 2513280
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD2618
direct productC2×D1309
unambiguous semidirect product(C2×C7)⋊D187
unambiguous semidirect product(C2×C11)⋊D119
unambiguous semidirect product(C2×C17)⋊D77

Splittings

Fitting, socleC2×C7×C11×C17 ⋊ C2
derived, HallC7×C11×C17 ⋊ C22
HallC11×C17 ⋊ C2×D7
HallC7×C17 ⋊ C2×D11
HallC7×C11 ⋊ C2×D17
SylowC17 ⋊ C2×D77
SylowC11 ⋊ C2×D119
SylowC7 ⋊ C2×D187

Subgroups

subgroupG/H
center, hypercenterC2D1309
commutator, hypocenterC7×C11×C17C22
FrattiniC1G
Fitting, socleC2×C7×C11×C17C2
LCSG ▷ C7×C11×C17
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1312 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C11⋊(C17⋊AGL(1,𝔽7)), D3×D1309, C2×D3927, …
maximal normal subgroup ofC2×C11⋊(C17⋊AGL(1,𝔽7)), C2×C3×D1309, C2×C7⋊(C17⋊AGL(1,𝔽11)), …
maximal quotient ofD3×D1309, C2×D3927, C2×C3×D1309, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5236, 21);