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C23×C3⋊(C11⋊Dic11) #45688987

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

Aliases

direct productC23×C3⋊(C11⋊Dic11)
unambiguous semidirect productC3⋊(C23×C11⋊Dic11)
unambiguous semidirect productC11⋊(C23×Dic33)

Splittings

derived, HallC3×C112 ⋊ C4×C23
HallC3×C112×C23 ⋊ C4
HallC112×C23 ⋊ Dic3
SylowC112 ⋊ Dic3×C23
HallC3×C23 ⋊ C11⋊Dic11
SylowC3 ⋊ C23×C11⋊Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C23C3⋊(C11⋊D11)
commutator, hypocenterC3×C112C4×C23
FrattiniC2C23×C3⋊(C11⋊D11)
Fitting, socle, prime radicalC2×C3×C112×C23C2
cosocleC2×C3×C112C2×C23
LCSG ▷ C3×C112
UCSC1 ◁ C2×C23

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33396

Conjugacy classes & character table

8418 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33396, 51);