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ΓL(1,𝔽8)×D211⋊C5 #56004685

order44310
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×D211⋊C5

Splittings

Fitting, socle, derived, HallC7×C211 ⋊ C2×C3×C5
HallΓL(1,𝔽8)×C211⋊C5 ⋊ C2
HallC7×D211⋊C5 ⋊ C3
HallΓL(1,𝔽8)×D211 ⋊ C5
HallC7×C211⋊C5 ⋊ C2×C3
HallΓL(1,𝔽8)×C211 ⋊ C2×C5
HallC7×D211 ⋊ C3×C5
HallC211⋊C5 ⋊ C2×ΓL(1,𝔽8)
HallD211 ⋊ C5×ΓL(1,𝔽8)
SylowC211 ⋊ C2×C5×ΓL(1,𝔽8)
SylowC7 ⋊ C3×D211⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C211C2×C3×C5
LCSG ▷ C7×C211
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

155 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(44310, 79);