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C4×ΓL(1,𝔽8)×C337 #43246707

order28308
automorphism?
homologyAbelianization (H1) = C3×C4×C337 · Schur multiplier (H2) = C1

Aliases

direct productC4×ΓL(1,𝔽8)×C337
unambiguous semidirect product(C4×C7)⋊(C3×C337)

Splittings

Fitting, HallC4×C7×C337 ⋊ C3
derived, SylowC7 ⋊ C3×C4×C337
HallC7×C337 ⋊ C3×C4
HallC4×C7 ⋊ C3×C337

Subgroups

subgroupG/H
center, hypercenterC4×C337ΓL(1,𝔽8)
commutator, hypocenterC7C3×C4×C337
FrattiniC2C2×ΓL(1,𝔽8)×C337
FittingC4×C7×C337C3
socleC2×C7×C337C2×C3
prime radicalC2×ΓL(1,𝔽8)×C337C2
cosocleC2×C7C2×C3×C337
LCSG ▷ C7
UCSC1 ◁ C4×C337

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9436

Conjugacy classes & character table

6740 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28308, 4);