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C41×D231 #34038824

order18942
automorphism?
homologyAbelianization (H1) = C2×C41 · Schur multiplier (H2) = C1

Aliases

direct productC41×D231
unambiguous semidirect productC3⋊(C41×D77)
unambiguous semidirect productC7⋊(C41×D33)
unambiguous semidirect productC11⋊(C41×D21)

Splittings

Fitting, socle, HallC3×C7×C11×C41 ⋊ C2
derived, HallC3×C7×C11 ⋊ C2×C41
HallC7×C11×C41 ⋊ D3
HallC3×C11×C41 ⋊ D7
HallC3×C7×C41 ⋊ D11
HallC11×C41 ⋊ D21
HallC7×C41 ⋊ D33
HallC3×C41 ⋊ D77
HallC7×C11 ⋊ D3×C41
HallC3×C11 ⋊ D7×C41
HallC3×C7 ⋊ D11×C41
SylowC11 ⋊ C41×D21
SylowC7 ⋊ C41×D33
SylowC3 ⋊ C41×D77

Subgroups

subgroupG/H
center, hypercenterC41D231
commutator, cosocle, hypocenterC3×C7×C11C2×C41
FrattiniC1G
Fitting, socleC3×C7×C11×C41C2
LCSG ▷ C3×C7×C11
UCSC1 ◁ C41

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9471

Conjugacy classes & character table

4797 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD41×D231, D11×C41×D21, D451⋊D21, …
maximal normal subgroup ofD41×D231, D11×C41×D21, D451⋊D21, …
maximal quotient ofC41×Dic231, C2×C41×D231

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18942, 16);