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C2×C5×(C112⋊C3)⋊C5 #31827620

order18150
automorphism?
homologyAbelianization (H1) = C2×C3×C52 · Schur multiplier (H2) = C5

Aliases

direct productC2×C5×(C112⋊C3)⋊C5
unambiguous semidirect product(C2×C112⋊C3)⋊C52
unambiguous semidirect product(C2×C5×C112⋊C3)⋊C5
unambiguous semidirect product(C2×C5×#10597243)⋊C3

Splittings

Fitting, socleC2×C5×C112 ⋊ C3×C5
derived, SylowC112 ⋊ C2×C3×C52
HallC2×C5×#10597243 ⋊ C3
HallC5×#10597243 ⋊ C2×C3
HallC2×C112⋊C3 ⋊ C52
HallC112⋊C3 ⋊ C2×C52
HallC2×C112 ⋊ C3×C52

Subgroups

subgroupG/H
center, hypercenterC2×C5(C112⋊C3)⋊C5
commutator, cosocle, hypocenterC112C2×C3×C52
FrattiniC1G
Fitting, socleC2×C5×C112C3×C5
LCSG ▷ C112
UCSC1 ◁ C2×C5

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 330

Conjugacy classes & character table

230 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#13089712⋊C5, C5×((C11⋊Dic11)⋊C3)⋊C5, #20299971⋊C5, …
maximal normal subgroup ofC5×#13089712⋊C5, C5×((C11⋊Dic11)⋊C3)⋊C5, #20299971⋊C5, …
maximal quotient ofC4×C5×(C112⋊C3)⋊C5, C22×C5×(C112⋊C3)⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18150, 104);