Finite Group Databasebeta

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C11×C11⋊((C19⋊C3)⋊C4) #42119945

order27588
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C11⋊((C19⋊C3)⋊C4)
unambiguous semidirect productC11⋊(C11×(C19⋊C3)⋊C4)
unambiguous semidirect product(C19⋊C3)⋊(C11×Dic11)
unambiguous semidirect productDic209⋊(C3×C11)
unambiguous semidirect product(C11×Dic209)⋊C3

Splittings

derivedC11×C19 ⋊ C3×C4×C11
HallC11×Dic209 ⋊ C3
HallC112×C19⋊C3 ⋊ C4
HallC112×C19 ⋊ C3×C4
SylowC112 ⋊ (C19⋊C3)⋊C4
HallC19⋊C3 ⋊ C11×Dic11
SylowC19 ⋊ C3×C11×Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C11C11⋊(D19⋊C3)
commutator, hypocenterC11×C19C3×C4×C11
FrattiniC2C11×C11⋊(D19⋊C3)
Fitting, socleC2×C112×C19C2×C3
prime radicalC2×C112×C19⋊C3C2
cosocleC2×C11×C19C2×C3×C11
LCSG ▷ C11×C19
UCSC1 ◁ C2×C11

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 836

Conjugacy classes & character table

1188 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27588, 37);