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Dic5×ΓL(1,𝔽8)×C79 #45684403

order33180
automorphism?
homologyAbelianization (H1) = C3×C4×C79 · Schur multiplier (H2) = C1

Aliases

direct productDic5×ΓL(1,𝔽8)×C79
unambiguous semidirect product(C7×Dic5)⋊(C3×C79)

Splittings

derived, HallC5×C7 ⋊ C3×C4×C79
HallC7×Dic5×C79 ⋊ C3
HallC5×ΓL(1,𝔽8)×C79 ⋊ C4
HallC5×C7×C79 ⋊ C3×C4
HallC7×C79 ⋊ C3×Dic5
HallC5×C79 ⋊ C4×ΓL(1,𝔽8)
HallC7×Dic5 ⋊ C3×C79
HallC5×ΓL(1,𝔽8) ⋊ C4×C79
SylowC7 ⋊ C3×Dic5×C79
SylowC5 ⋊ C4×ΓL(1,𝔽8)×C79

Subgroups

subgroupG/H
center, hypercenterC2×C79D5×ΓL(1,𝔽8)
commutator, hypocenterC5×C7C3×C4×C79
FrattiniC2D5×ΓL(1,𝔽8)×C79
Fitting, socleC2×C5×C7×C79C2×C3
prime radicalC2×C5×ΓL(1,𝔽8)×C79C2
cosocleC2×C5×C7C2×C3×C79
LCSG ▷ C5×C7
UCSC1 ◁ C2×C79

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11060

Conjugacy classes & character table

3160 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33180, 34);