Finite Group Databasebeta

← Prev (#28412897) Next (#28412899) →

C25×ΓL(1,𝔽8)⋊Dic7 #28412898

order14700
automorphism?
homologyAbelianization (H1) = C3×C4×C25 · Schur multiplier (H2) = C1

Aliases

direct productC25×ΓL(1,𝔽8)⋊Dic7
unambiguous semidirect productΓL(1,𝔽8)⋊(C25×Dic7)

Splittings

derived, SylowC72 ⋊ C3×C4×C25
HallC25×C7⋊Dic7 ⋊ C3
HallC7×ΓL(1,𝔽8)×C25 ⋊ C4
HallC72×C25 ⋊ C3×C4
HallC7⋊Dic7 ⋊ C3×C25
HallC7×ΓL(1,𝔽8) ⋊ C4×C25

Subgroups

subgroupG/H
center, hypercenterC2×C25ΓL(1,𝔽8)⋊D7
commutator, hypocenterC72C3×C4×C25
FrattiniC2×C5C5×ΓL(1,𝔽8)⋊D7
FittingC2×C72×C25C2×C3
socle, cosocleC2×C5×C72C2×C3×C5
prime radicalC2×C5×C7×ΓL(1,𝔽8)C2×C5
LCSG ▷ C72
UCSC1 ◁ C2×C25

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 77);