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C2×D1995 #22547749

order7980
automorphismAut(G) order 3447360
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD3990
direct productC2×D1995
unambiguous semidirect product(C2×C3)⋊D665
unambiguous semidirect product(C2×C5)⋊D399
unambiguous semidirect product(C2×C7)⋊D285
unambiguous semidirect product(C2×C19)⋊D105

Splittings

Fitting, socleC2×C3×C5×C7×C19 ⋊ C2
derived, HallC3×C5×C7×C19 ⋊ C22
HallC5×C7×C19 ⋊ C2×D3
HallC3×C7×C19 ⋊ C2×D5
HallC3×C5×C19 ⋊ C2×D7
HallC7×C19 ⋊ C2×D15
HallC3×C5×C7 ⋊ C2×D19
HallC5×C19 ⋊ C2×D21
HallC3×C19 ⋊ C2×D35
HallC5×C7 ⋊ C2×D57
HallC3×C7 ⋊ C2×D95
SylowC19 ⋊ C2×D105
HallC3×C5 ⋊ C2×D133
SylowC7 ⋊ C2×D285
SylowC5 ⋊ C2×D399
SylowC3 ⋊ C2×D665

Subgroups

subgroupG/H
center, hypercenterC2D1995
commutator, hypocenterC3×C5×C7×C19C22
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C19C2
LCSG ▷ C3×C5×C7×C19
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1998 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×D5985, C2×C3⋊(C5⋊#11716327), C2×C3⋊(C5⋊#11716328), …
maximal normal subgroup ofC2×C3⋊(C5⋊#11716327), C2×C3⋊(C5⋊#11716328), C2×C3⋊(C5⋊(ΓL(1,𝔽8)⋊D19)), …
maximal quotient ofC2×D5985, D3×D1995, C2×C3×D1995, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 174);