Finite Group Databasebeta

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C2×C7⋊C9×C43⋊C7 #49181532

order37926
automorphism?
homologyAbelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC2×C7⋊C9×C43⋊C7
unambiguous semidirect product(C2×C7)⋊(C9×C43⋊C7)
unambiguous semidirect product(C2×C43×C7⋊C9)⋊C7

Splittings

derivedC7×C43 ⋊ C2×C7×C9
HallC2×C7×C43⋊C7 ⋊ C9
HallC7×C43⋊C7 ⋊ C2×C9
HallC2×C43 ⋊ C7×C7⋊C9
SylowC43 ⋊ C2×C7×C7⋊C9

Subgroups

subgroupG/H
center, hypercenterC2×C3ΓL(1,𝔽8)×C43⋊C7
commutator, hypocenterC7×C43C2×C7×C9
FrattiniC3C2×ΓL(1,𝔽8)×C43⋊C7
Fitting, socleC2×C3×C7×C43C3×C7
prime radicalC2×C3×C7×C43⋊C7C3
cosocleC3×C7×C43C2×C3×C7
LCSG ▷ C7×C43
UCSC1 ◁ C2×C3

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5418

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37926, 105);