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C4×(C337⋊C3)⋊C7 #43246710

order28308
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC4×(C337⋊C3)⋊C7
unambiguous semidirect product(C4×C337⋊C3)⋊C7
unambiguous semidirect product(C4×C337⋊C7)⋊C3

Splittings

Fitting, HallC4×C337 ⋊ C3×C7
derived, SylowC337 ⋊ C3×C4×C7
HallC4×C337⋊C7 ⋊ C3
HallC4×C337⋊C3 ⋊ C7
HallC337⋊C7 ⋊ C3×C4
HallC337⋊C3 ⋊ C4×C7

Subgroups

subgroupG/H
center, hypercenterC4(C337⋊C3)⋊C7
commutator, hypocenterC337C3×C4×C7
FrattiniC2C2×(C337⋊C3)⋊C7
FittingC4×C337C3×C7
socle, cosocleC2×C337C2×C3×C7
prime radicalC2×(C337⋊C3)⋊C7C2
LCSG ▷ C337
UCSC1 ◁ C4

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1348

Conjugacy classes & character table

148 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28308, 7);