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C2×(C181⋊C3)⋊C5 #19129502

order5430
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC2×(C181⋊C3)⋊C5
unambiguous semidirect product(C2×C181⋊C3)⋊C5
unambiguous semidirect product(C2×C181⋊C5)⋊C3

Splittings

Fitting, socle, HallC2×C181 ⋊ C3×C5
derived, SylowC181 ⋊ C2×C3×C5
HallC2×C181⋊C5 ⋊ C3
HallC2×C181⋊C3 ⋊ C5
HallC181⋊C5 ⋊ C2×C3
HallC181⋊C3 ⋊ C2×C5

Subgroups

subgroupG/H
center, hypercenterC2(C181⋊C3)⋊C5
commutator, hypocenterC181C2×C3×C5
FrattiniC1G
Fitting, socleC2×C181C3×C5
LCSG ▷ C181
UCSC1 ◁ C2

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

54 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×(C181⋊C3)⋊C5, (Dic181⋊C3)⋊C5, C2×(D181⋊C3)⋊C5, …
maximal normal subgroup ofC4×(C181⋊C3)⋊C5, (Dic181⋊C3)⋊C5, C2×(D181⋊C3)⋊C5, …
maximal quotient ofC4×(C181⋊C3)⋊C5, C22×(C181⋊C3)⋊C5, C2×#13108656⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5430, 4);