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ΓL(1,𝔽8)×C25×Dic11 #37528216

order23100
automorphism?
homologyAbelianization (H1) = C3×C4×C25 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×C25×Dic11
unambiguous semidirect product(C7×C25×Dic11)⋊C3

Splittings

derived, HallC7×C11 ⋊ C3×C4×C25
HallC7×C25×Dic11 ⋊ C3
HallC11×ΓL(1,𝔽8)×C25 ⋊ C4
HallC7×C11×C25 ⋊ C3×C4
HallC7×Dic11 ⋊ C3×C25
HallC11×C25 ⋊ C4×ΓL(1,𝔽8)
HallC11×ΓL(1,𝔽8) ⋊ C4×C25
HallC7×C25 ⋊ C3×Dic11
SylowC11 ⋊ C4×ΓL(1,𝔽8)×C25
SylowC7 ⋊ C3×C25×Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C25ΓL(1,𝔽8)×D11
commutator, hypocenterC7×C11C3×C4×C25
FrattiniC2×C5C5×ΓL(1,𝔽8)×D11
FittingC2×C7×C11×C25C2×C3
socle, cosocleC2×C5×C7×C11C2×C3×C5
prime radicalC2×C5×C11×ΓL(1,𝔽8)C2×C5
LCSG ▷ C7×C11
UCSC1 ◁ C2×C25

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7700

Conjugacy classes & character table

1750 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 27);