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#72179441

order65274
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

Fitting, socle, derived, HallC23×C43 ⋊ C2×C3×C11
HallC43⋊C3×C23⋊C11 ⋊ C2
HallC43⋊AGL(1,𝔽23) ⋊ C3
HallC43×C23⋊C11 ⋊ C2×C3
HallC23⋊(D43⋊C3) ⋊ C11
HallC23×C43⋊C3 ⋊ C2×C11
HallD989 ⋊ C3×C11
HallC23⋊C11 ⋊ D43⋊C3
HallC43⋊C3 ⋊ AGL(1,𝔽23)
SylowC43 ⋊ C3×AGL(1,𝔽23)
SylowC23 ⋊ C11×D43⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC23×C43C2×C3×C11
LCSG ▷ C23×C43
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,3,11,23,43|d^a=d^22,e^a=e^42,e^b=e^36,d^c=d^2

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(65274, 36);