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C5×AGL(1,𝔽7)×C211 #56004658

order44310
isoclinismisoclinic class of AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C211 · Schur multiplier (H2) = C1

Aliases

direct productC5×AGL(1,𝔽7)×C211

Splittings

Fitting, socle, HallC5×C7×C211 ⋊ C2×C3
derived, SylowC7 ⋊ C2×C3×C5×C211
HallC5×ΓL(1,𝔽8)×C211 ⋊ C2
HallC5×D7×C211 ⋊ C3
HallΓL(1,𝔽8)×C211 ⋊ C2×C5
HallD7×C211 ⋊ C3×C5
HallC7×C211 ⋊ C2×C3×C5
HallC5×ΓL(1,𝔽8) ⋊ C2×C211
HallC5×D7 ⋊ C3×C211
HallC5×C7 ⋊ C2×C3×C211
HallΓL(1,𝔽8) ⋊ C2×C5×C211
HallD7 ⋊ C3×C5×C211

Subgroups

subgroupG/H
center, hypercenterC5×C211AGL(1,𝔽7)
commutator, cosocle, hypocenterC7C2×C3×C5×C211
FrattiniC1G
Fitting, socleC5×C7×C211C2×C3
LCSG ▷ C7
UCSC1 ◁ C5×C211

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7385 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(44310, 52);