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C2×ΓL(1,𝔽8)2×C41 #49116333

order36162
automorphism?
homologyAbelianization (H1) = C2×C32×C41 · Schur multiplier (H2) = C3

Aliases

direct productC2×ΓL(1,𝔽8)2×C41
unambiguous semidirect product(C2×C7×ΓL(1,𝔽8))⋊(C3×C41)
unambiguous semidirect product(C2×#3861)⋊(C3×C41)
unambiguous semidirect product(C2×#3862)⋊(C3×C41)
unambiguous semidirect product(C2×C41×#3862)⋊C3
unambiguous semidirect product(C2×C7×ΓL(1,𝔽8)×C41)⋊C3
unambiguous semidirect product(C2×C41×#3861)⋊C3

Splittings

Fitting, socle, HallC2×C72×C41 ⋊ C32
derived, SylowC72 ⋊ C2×C32×C41
HallC72×C41 ⋊ C2×C32
HallC2×C72 ⋊ C32×C41

Subgroups

subgroupG/H
center, hypercenterC2×C41ΓL(1,𝔽8)2
commutator, cosocle, hypocenterC72C2×C32×C41
FrattiniC1G
Fitting, socleC2×C72×C41C32
LCSG ▷ C72
UCSC1 ◁ C2×C41

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1722

Conjugacy classes & character table

2050 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36162, 75);