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C3×C7×(C11⋊C5)⋊Dic5 #37528340

order23100
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×(C11⋊C5)⋊Dic5
unambiguous semidirect product(C11⋊C5)⋊(C3×C7×Dic5)
unambiguous semidirect productDic55⋊(C3×C5×C7)
unambiguous semidirect product(C3×Dic55)⋊(C5×C7)
unambiguous semidirect product(C3×C7×Dic55)⋊C5

Splittings

derivedC5×C11 ⋊ C3×C4×C5×C7
HallC3×C5×C7×C11⋊C5 ⋊ C4
HallC5×C7×C11⋊C5 ⋊ C3×C4
HallC3×C5×C11⋊C5 ⋊ C4×C7
HallC5×C11⋊C5 ⋊ C3×C4×C7
HallC3×C7×C11 ⋊ C5×Dic5
HallC7×C11 ⋊ C3×C5×Dic5
HallC3×C11 ⋊ C5×C7×Dic5
SylowC11 ⋊ C3×C5×C7×Dic5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7C5⋊AGL(1,𝔽11)
commutator, hypocenterC5×C11C3×C4×C5×C7
FrattiniC2C3×C7×C5⋊AGL(1,𝔽11)
Fitting, socleC2×C3×C5×C7×C11C2×C5
prime radicalC2×C3×C5×C7×C11⋊C5C2
cosocleC2×C5×C11C2×C3×C5×C7
LCSG ▷ C5×C11
UCSC1 ◁ C2×C3×C7

128 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 56 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) = 4620

Conjugacy classes & character table

1050 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 151);