Finite Group Databasebeta

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C11×Dic3×C23⋊C11 #45688976

order33396
automorphism?
homologyAbelianization (H1) = C4×C112 · Schur multiplier (H2) = C11

Aliases

direct productC11×Dic3×C23⋊C11
unambiguous semidirect productC3⋊(C4×C11×C23⋊C11)
unambiguous semidirect product(Dic3×C23)⋊C112
unambiguous semidirect product(C11×Dic3×C23)⋊C11

Splittings

derived, HallC3×C23 ⋊ C4×C112
HallC3×C11×C23⋊C11 ⋊ C4
HallDic3×C23 ⋊ C112
SylowC23 ⋊ C112×Dic3
SylowC3 ⋊ C4×C11×C23⋊C11

Subgroups

subgroupG/H
center, hypercenterC2×C11D3×C23⋊C11
commutator, hypocenterC3×C23C4×C112
FrattiniC2D3×C11×C23⋊C11
Fitting, socleC2×C3×C11×C23C2×C11
prime radicalC2×C3×C11×C23⋊C11C2
cosocleC2×C3×C23C2×C112
LCSG ▷ C3×C23
UCSC1 ◁ C2×C11

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3036

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33396, 40);