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C5×ΓL(1,𝔽8)⋊Dic71 #44447153

order29820
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×ΓL(1,𝔽8)⋊Dic71
unambiguous semidirect productΓL(1,𝔽8)⋊(C5×Dic71)
unambiguous semidirect product(C5×Dic497)⋊C3

Splittings

derived, HallC7×C71 ⋊ C3×C4×C5
HallC5×Dic497 ⋊ C3
HallC5×ΓL(1,𝔽8)×C71 ⋊ C4
HallC5×C7×C71 ⋊ C3×C4
HallDic497 ⋊ C3×C5
HallΓL(1,𝔽8)×C71 ⋊ C4×C5
HallC5×C71 ⋊ ΓL(1,𝔽8)⋊C4
HallC5×ΓL(1,𝔽8) ⋊ Dic71
SylowC71 ⋊ C5×ΓL(1,𝔽8)⋊C4
HallC5×C7 ⋊ C3×Dic71
HallΓL(1,𝔽8) ⋊ C5×Dic71
SylowC7 ⋊ C3×C5×Dic71

Subgroups

subgroupG/H
center, hypercenterC2×C5ΓL(1,𝔽8)⋊D71
commutator, hypocenterC7×C71C3×C4×C5
FrattiniC2C5×ΓL(1,𝔽8)⋊D71
Fitting, socleC2×C5×C7×C71C2×C3
prime radicalC2×C5×ΓL(1,𝔽8)×C71C2
cosocleC2×C7×C71C2×C3×C5
LCSG ▷ C7×C71
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9940

Conjugacy classes & character table

1820 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 41);