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C2×C3×C5×C112⋊C3 #24926196

order10890
isoclinismisoclinic class of C112⋊C3
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3×C11

Aliases

direct productC2×C3×C5×C112⋊C3
unambiguous semidirect product(C2×C5×C112)⋊C32
unambiguous semidirect product(C2×C3×C5×C112)⋊C3

Splittings

Fitting, socleC2×C3×C5×C112 ⋊ C3
derived, SylowC112 ⋊ C2×C32×C5
HallC2×C5×C112 ⋊ C32
HallC5×C112 ⋊ C2×C32
HallC2×C112 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5C112⋊C3
commutator, cosocle, hypocenterC112C2×C32×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C112C3
LCSG ▷ C112
UCSC1 ◁ C2×C3×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1290 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×#13089712, C3×C5×(C11⋊Dic11)⋊C3, C3×#20299971, …
maximal normal subgroup ofC3×C5×#13089712, C3×C5×(C11⋊Dic11)⋊C3, C3×#20299971, …
maximal quotient ofC3×C4×C5×C112⋊C3, C22×C3×C5×C112⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10890, 145);