Finite Group Databasebeta

← Prev (#29509582) Next (#29509584) →

ΓL(1,𝔽8)×#10625191 #29509583

order15540
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×#10625191

Splittings

Fitting, socle, derived, HallC5×C7×C37 ⋊ C3×C4
HallC7×#10625191 ⋊ C3
HallC5×ΓL(1,𝔽8)×C37 ⋊ C4
HallΓL(1,𝔽8)×C37 ⋊ AGL(1,𝔽5)
HallC7×C37 ⋊ C3×AGL(1,𝔽5)
HallC5×C37 ⋊ C4×ΓL(1,𝔽8)
HallC5×ΓL(1,𝔽8) ⋊ #3866
SylowC37 ⋊ AGL(1,𝔽5)×ΓL(1,𝔽8)
HallC5×C7 ⋊ C3×#3866
SylowC7 ⋊ C3×#10625191
SylowC5 ⋊ ΓL(1,𝔽8)×#3866

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C7×C37C3×C4
prime radicalΓL(1,𝔽8)×D185C2
cosocleC7×D185C2×C3
LCSG ▷ C5×C7×C37
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1295

Conjugacy classes & character table

250 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15540, 85);