Finite Group Databasebeta

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C3×C5×C11×Dic57 #49178493

order37620
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C11×Dic57
unambiguous semidirect productC3⋊(C3×C5×C11×Dic19)

Splittings

derivedC3×C19 ⋊ C3×C4×C5×C11
HallC32×C5×C11×C19 ⋊ C4
HallC32×C11×C19 ⋊ C4×C5
HallC5×C11×C19 ⋊ C3×Dic3
HallC32×C5×C19 ⋊ C4×C11
HallC32×C5×C11 ⋊ Dic19
HallC11×C19 ⋊ C3×C5×Dic3
HallC32×C19 ⋊ C4×C5×C11
HallC32×C11 ⋊ C5×Dic19
HallC5×C19 ⋊ C3×C11×Dic3
HallC32×C5 ⋊ C11×Dic19
SylowC19 ⋊ C3×C5×C11×Dic3
SylowC32 ⋊ C5×C11×Dic19

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C11D57
commutator, hypocenterC3×C19C3×C4×C5×C11
FrattiniC2C3×C5×C11×D57
Fitting, socle, prime radicalC2×C32×C5×C11×C19C2
cosocleC2×C3×C19C2×C3×C5×C11
LCSG ▷ C3×C19
UCSC1 ◁ C2×C3×C5×C11

112 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 72 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

9900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 202);