Finite Group Databasebeta

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C11×C11⋊(#1043⋊C3) #49137573

order36300
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C11⋊(#1043⋊C3)
unambiguous semidirect productC11⋊(C11×#1043⋊C3)
unambiguous semidirect product(C11⋊#1043)⋊(C3×C11)
unambiguous semidirect product(C11×C11⋊#1043)⋊C3

Splittings

Fitting, socle, HallC52×C112 ⋊ C3×C4
derivedC52×C11 ⋊ C3×C4×C11
HallC11×C11⋊#1043 ⋊ C3
HallC112×C52⋊C3 ⋊ C4
SylowC112 ⋊ #1043⋊C3
HallC52⋊C3 ⋊ C11×Dic11
SylowC52 ⋊ C3×C11×Dic11

Subgroups

subgroupG/H
center, hypercenterC11C11⋊(#1043⋊C3)
commutator, hypocenterC52×C11C3×C4×C11
FrattiniC1G
Fitting, socleC52×C112C3×C4
prime radicalC112×(C5⋊D5)⋊C3C2
cosocleC11×C5⋊D5C2×C3×C11
LCSG ▷ C52×C11
UCSC1 ◁ C11

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 330

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 709);