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C22⋊ΓL(1,𝔽8)×C11⋊C25 #37528240

order23100
automorphism?
homologyAbelianization (H1) = C3×C25 · Schur multiplier (H2) = C2

Aliases

direct productC22⋊ΓL(1,𝔽8)×C11⋊C25
unambiguous semidirect productC22⋊(ΓL(1,𝔽8)×C11⋊C25)
unambiguous semidirect productC7⋊(A4×C11⋊C25)
unambiguous semidirect productC11⋊(C25×C22⋊ΓL(1,𝔽8))
unambiguous semidirect product(C11×C22⋊ΓL(1,𝔽8))⋊C25
unambiguous semidirect product(C22×C11⋊C25)⋊ΓL(1,𝔽8)
unambiguous semidirect product(C7×C11⋊C25)⋊A4

Splittings

derived, HallC22×C7×C11 ⋊ C3×C25
HallC22×C7×C11⋊C25 ⋊ C3
HallC7×C11⋊C25 ⋊ A4
HallC22×C11⋊C25 ⋊ ΓL(1,𝔽8)
HallC11×C22⋊ΓL(1,𝔽8) ⋊ C25
HallC7×C11 ⋊ A4×C25
HallC22×C11 ⋊ ΓL(1,𝔽8)×C25
HallC22×C7 ⋊ C3×C11⋊C25
SylowC11 ⋊ C25×C22⋊ΓL(1,𝔽8)
SylowC7 ⋊ A4×C11⋊C25
SylowC22 ⋊ ΓL(1,𝔽8)×C11⋊C25

Subgroups

subgroupG/H
center, Frattini, hypercenterC5C11⋊C5×C22⋊ΓL(1,𝔽8)
commutator, hypocenterC22×C7×C11C3×C25
Fitting, socle, cosocleC22×C5×C7×C11C3×C5
prime radicalC5×C11×C22⋊ΓL(1,𝔽8)C5
LCSG ▷ C22×C7×C11
UCSC1 ◁ C5

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7700

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 51);