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C11×(C11⋊C5)⋊Dic5 #27130849

order12100
automorphism?
homologyAbelianization (H1) = C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×(C11⋊C5)⋊Dic5
unambiguous semidirect product(C11⋊C5)⋊(C11×Dic5)
unambiguous semidirect productDic55⋊(C5×C11)

Splittings

derivedC5×C11 ⋊ C4×C5×C11
HallC5×C11×C11⋊C5 ⋊ C4
SylowC112 ⋊ C5×Dic5

Subgroups

subgroupG/H
center, hypercenterC2×C11C5⋊AGL(1,𝔽11)
commutator, hypocenterC5×C11C4×C5×C11
FrattiniC2C11×C5⋊AGL(1,𝔽11)
Fitting, socleC2×C5×C112C2×C5
prime radicalC2×C5×C11×C11⋊C5C2
cosocleC2×C5×C11C2×C5×C11
LCSG ▷ C5×C11
UCSC1 ◁ C2×C11

68 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

550 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C11×(C11⋊C5)⋊Dic5, C11×C3⋊((C11⋊C5)⋊Dic5)
maximal normal subgroup ofC3×C11×(C11⋊C5)⋊Dic5
maximal quotient ofC3×C11×(C11⋊C5)⋊Dic5, C11×C3⋊((C11⋊C5)⋊Dic5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12100, 128);