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C23×(C11⋊Dic11)⋊C3 #45688982

order33396
automorphism?
homologyAbelianization (H1) = C3×C4×C23 · Schur multiplier (H2) = C11

Aliases

direct productC23×(C11⋊Dic11)⋊C3
unambiguous semidirect product(C11⋊Dic11)⋊(C3×C23)
unambiguous semidirect product(C23×C11⋊Dic11)⋊C3

Splittings

derived, SylowC112 ⋊ C3×C4×C23
HallC23×C11⋊Dic11 ⋊ C3
HallC23×C112⋊C3 ⋊ C4
HallC112×C23 ⋊ C3×C4
HallC11⋊Dic11 ⋊ C3×C23
HallC112⋊C3 ⋊ C4×C23

Subgroups

subgroupG/H
center, hypercenterC2×C23(C11⋊D11)⋊C3
commutator, hypocenterC112C3×C4×C23
FrattiniC2C23×(C11⋊D11)⋊C3
Fitting, socleC2×C112×C23C2×C3
prime radicalC2×C23×C112⋊C3C2
cosocleC2×C112C2×C3×C23
LCSG ▷ C112
UCSC1 ◁ C2×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3036

Conjugacy classes & character table

1196 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33396, 46);