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C52×C11×ΓL(1,𝔽8)⋊C4 #37528352

order23100
automorphism?
homologyAbelianization (H1) = C3×C4×C52×C11 · Schur multiplier (H2) = C5

Aliases

direct productC52×C11×ΓL(1,𝔽8)⋊C4
unambiguous semidirect productΓL(1,𝔽8)⋊(C4×C52×C11)
unambiguous semidirect productDic7⋊(C3×C52×C11)
unambiguous semidirect product(C5×Dic7)⋊(C3×C5×C11)

Splittings

derived, SylowC7 ⋊ C3×C4×C52×C11
HallC52×C11×Dic7 ⋊ C3
HallC52×C11×ΓL(1,𝔽8) ⋊ C4
HallC52×C7×C11 ⋊ C3×C4
HallC52×Dic7 ⋊ C3×C11
HallC52×ΓL(1,𝔽8) ⋊ C4×C11
HallC11×Dic7 ⋊ C3×C52
HallC11×ΓL(1,𝔽8) ⋊ C4×C52
HallC52×C7 ⋊ C3×C4×C11
HallC7×C11 ⋊ C3×C4×C52
HallDic7 ⋊ C3×C52×C11
HallΓL(1,𝔽8) ⋊ C4×C52×C11

Subgroups

subgroupG/H
center, hypercenterC2×C52×C11AGL(1,𝔽7)
commutator, hypocenterC7C3×C4×C52×C11
FrattiniC2C52×C11×AGL(1,𝔽7)
Fitting, socleC2×C52×C7×C11C2×C3
prime radicalC2×C52×C11×ΓL(1,𝔽8)C2
cosocleC2×C7C2×C3×C52×C11
LCSG ▷ C7
UCSC1 ◁ C2×C52×C11

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7700

Conjugacy classes & character table

3850 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 163);