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C4×C11×ΓL(1,𝔽8)×C25 #37528192

order23100
automorphism?
homologyAbelianization (H1) = C3×C4×C11×C25 · Schur multiplier (H2) = C1

Aliases

direct productC4×C11×ΓL(1,𝔽8)×C25
unambiguous semidirect product(C4×C7)⋊(C3×C11×C25)
unambiguous semidirect product(C4×C7×C25)⋊(C3×C11)
unambiguous semidirect product(C4×C7×C11×C25)⋊C3

Splittings

Fitting, HallC4×C7×C11×C25 ⋊ C3
derived, SylowC7 ⋊ C3×C4×C11×C25
HallC7×C11×C25 ⋊ C3×C4
HallC4×C7×C25 ⋊ C3×C11
HallC4×C7×C11 ⋊ C3×C25
HallC7×C25 ⋊ C3×C4×C11
HallC7×C11 ⋊ C3×C4×C25
HallC4×C7 ⋊ C3×C11×C25

Subgroups

subgroupG/H
center, hypercenterC4×C11×C25ΓL(1,𝔽8)
commutator, hypocenterC7C3×C4×C11×C25
FrattiniC2×C5C2×C5×C11×ΓL(1,𝔽8)
FittingC4×C7×C11×C25C3
socleC2×C5×C7×C11C2×C3×C5
prime radicalC2×C5×C11×ΓL(1,𝔽8)C2×C5
cosocleC2×C5×C7C2×C3×C5×C11
LCSG ▷ C7
UCSC1 ◁ C4×C11×C25

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7700

Conjugacy classes & character table

5500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 3);