Finite Group Databasebeta

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C11×C3⋊((C19⋊C3)⋊Dic5) #49178473

order37620
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C3⋊((C19⋊C3)⋊Dic5)
unambiguous semidirect productC3⋊(C11×(C19⋊C3)⋊Dic5)
unambiguous semidirect product(C19⋊C3)⋊(C11×Dic15)
unambiguous semidirect productDic285⋊(C3×C11)
unambiguous semidirect product(C11×Dic285)⋊C3

Splittings

derivedC3×C5×C19 ⋊ C3×C4×C11
HallC3×C5×C11×C19⋊C3 ⋊ C4
HallC3×C11×C19⋊C3 ⋊ Dic5
HallC5×C11×C19 ⋊ C3×Dic3
HallC3×C5×C19⋊C3 ⋊ C4×C11
HallC11×C19 ⋊ C3×Dic15
HallC3×C19⋊C3 ⋊ C11×Dic5
HallC5×C19 ⋊ C3×C11×Dic3
HallC5×C11 ⋊ C3⋊((C19⋊C3)⋊C4)
SylowC19 ⋊ C3×C11×Dic15
SylowC5 ⋊ C11×C3⋊((C19⋊C3)⋊C4)

Subgroups

subgroupG/H
center, hypercenterC2×C11C3⋊(C5⋊(D19⋊C3))
commutator, hypocenterC3×C5×C19C3×C4×C11
FrattiniC2C11×C3⋊(C5⋊(D19⋊C3))
Fitting, socleC2×C3×C5×C11×C19C2×C3
prime radicalC2×C3×C5×C11×C19⋊C3C2
cosocleC2×C3×C5×C19C2×C3×C11
LCSG ▷ C3×C5×C19
UCSC1 ◁ C2×C11

112 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12540

Conjugacy classes & character table

1584 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 182);