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C11×ΓL(1,𝔽8)⋊Dic25 #37528221

order23100
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×ΓL(1,𝔽8)⋊Dic25
unambiguous semidirect productΓL(1,𝔽8)⋊(C11×Dic25)
unambiguous semidirect productDic175⋊(C3×C11)
unambiguous semidirect product(C11×Dic175)⋊C3

Splittings

derived, HallC7×C25 ⋊ C3×C4×C11
HallC11×Dic175 ⋊ C3
HallC11×ΓL(1,𝔽8)×C25 ⋊ C4
HallC7×C11×C25 ⋊ C3×C4
HallDic175 ⋊ C3×C11
HallΓL(1,𝔽8)×C25 ⋊ C4×C11
HallC11×C25 ⋊ ΓL(1,𝔽8)⋊C4
HallC11×ΓL(1,𝔽8) ⋊ Dic25
HallC7×C11 ⋊ C3×Dic25
SylowC25 ⋊ C11×ΓL(1,𝔽8)⋊C4
HallΓL(1,𝔽8) ⋊ C11×Dic25
SylowC7 ⋊ C3×C11×Dic25

Subgroups

subgroupG/H
center, hypercenterC2×C11ΓL(1,𝔽8)⋊D25
commutator, hypocenterC7×C25C3×C4×C11
FrattiniC2×C5C11×C5⋊AGL(1,𝔽7)
FittingC2×C7×C11×C25C2×C3
socleC2×C5×C7×C11C3×D5
prime radicalC2×C5×C11×ΓL(1,𝔽8)D5
cosocleC2×C7×C25C2×C3×C11
LCSG ▷ C7×C25
UCSC1 ◁ C2×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7700

Conjugacy classes & character table

1474 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 32);