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C4×C7×ΓL(1,𝔽8)×C31 #32912114

order18228
automorphism?
homologyAbelianization (H1) = C3×C4×C7×C31 · Schur multiplier (H2) = C1

Aliases

direct productC4×C7×ΓL(1,𝔽8)×C31
unambiguous semidirect product(C4×C7)⋊(C3×C7×C31)

Splittings

Fitting, HallC4×C72×C31 ⋊ C3
derivedC7 ⋊ C3×C4×C7×C31
HallC72×C31 ⋊ C3×C4
HallC4×C72 ⋊ C3×C31
SylowC72 ⋊ C3×C4×C31

Subgroups

subgroupG/H
center, hypercenterC4×C7×C31ΓL(1,𝔽8)
commutator, hypocenterC7C3×C4×C7×C31
FrattiniC2C2×C7×ΓL(1,𝔽8)×C31
FittingC4×C72×C31C3
socleC2×C72×C31C2×C3
prime radicalC2×C7×ΓL(1,𝔽8)×C31C2
cosocleC2×C7C2×C3×C7×C31
LCSG ▷ C7
UCSC1 ◁ C4×C7×C31

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2604

Conjugacy classes & character table

4340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18228, 122);