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C2×C5×D97⋊C3 #19154147

order5820
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D97⋊C3
unambiguous semidirect productD97⋊(C2×C3×C5)
unambiguous semidirect product(C97⋊C3)⋊(C22×C5)
unambiguous semidirect product(C2×D97)⋊(C3×C5)
unambiguous semidirect product(C2×C97⋊C3)⋊(C2×C5)
unambiguous semidirect product(C2×C5×D97)⋊C3

Splittings

Fitting, socleC2×C5×C97 ⋊ C2×C3
derived, SylowC97 ⋊ C22×C3×C5
HallC2×C5×D97 ⋊ C3
HallC5×C97⋊C3 ⋊ C22
HallC5×C97 ⋊ C22×C3
HallC2×D97 ⋊ C3×C5
HallC97⋊C3 ⋊ C22×C5

Subgroups

subgroupG/H
center, hypercenterC2×C5D97⋊C3
commutator, hypocenterC97C22×C3×C5
FrattiniC1G
Fitting, socleC2×C5×C97C2×C3
LCSG ▷ C97
UCSC1 ◁ C2×C5

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D3×D97⋊C3, C2×C3×C5×D97⋊C3, C2×C5×C3⋊(D97⋊C3), …
maximal normal subgroup ofC2×C3×C5×D97⋊C3, C2×C25×D97⋊C3, C2×C52×D97⋊C3
maximal quotient ofC2×C5×D97⋊C9, C5×D3×D97⋊C3, C2×C3×C5×D97⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5820, 21);