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ΓL(1,𝔽8)⋊C4×C11⋊C25 #37528224

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

Aliases

direct productΓL(1,𝔽8)⋊C4×C11⋊C25
unambiguous semidirect productΓL(1,𝔽8)⋊(C4×C11⋊C25)
unambiguous semidirect productDic7⋊(C3×C11⋊C25)
unambiguous semidirect product(C11×ΓL(1,𝔽8)⋊C4)⋊C25
unambiguous semidirect product(Dic7×C11⋊C25)⋊C3

Splittings

derived, HallC7×C11 ⋊ C3×C4×C25
HallDic7×C11⋊C25 ⋊ C3
HallΓL(1,𝔽8)×C11⋊C25 ⋊ C4
HallC7×C11⋊C25 ⋊ C3×C4
HallC11×ΓL(1,𝔽8)⋊C4 ⋊ C25
HallC11×Dic7 ⋊ C3×C25
HallC11×ΓL(1,𝔽8) ⋊ C4×C25
HallDic7 ⋊ C3×C11⋊C25
HallΓL(1,𝔽8) ⋊ C4×C11⋊C25
SylowC11 ⋊ C25×ΓL(1,𝔽8)⋊C4
SylowC7 ⋊ C3×C4×C11⋊C25

Subgroups

subgroupG/H
center, Frattini, hypercenterC2×C5AGL(1,𝔽7)×C11⋊C5
commutator, hypocenterC7×C11C3×C4×C25
Fitting, socle, cosocleC2×C5×C7×C11C2×C3×C5
prime radicalC2×C5×C11×ΓL(1,𝔽8)C2×C5
LCSG ▷ C7×C11
UCSC1 ◁ C2×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7700

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 35);