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C5×C7×ΓL(1,𝔽8)×D23 #46798924

order33810
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×ΓL(1,𝔽8)×D23
unambiguous semidirect productC23⋊(C2×C5×C7×ΓL(1,𝔽8))
unambiguous semidirect product(C7×D23)⋊(C3×C5×C7)
unambiguous semidirect product(C5×C7×D23)⋊(C3×C7)

Splittings

Fitting, socle, HallC5×C72×C23 ⋊ C2×C3
derivedC7×C23 ⋊ C2×C3×C5×C7
HallC5×C7×ΓL(1,𝔽8)×C23 ⋊ C2
HallC5×C72×D23 ⋊ C3
HallC7×ΓL(1,𝔽8)×C23 ⋊ C2×C5
HallC72×D23 ⋊ C3×C5
HallC72×C23 ⋊ C2×C3×C5
HallC5×C72 ⋊ C3×D23
HallC5×C23 ⋊ C2×C7×ΓL(1,𝔽8)
SylowC72 ⋊ C3×C5×D23
SylowC23 ⋊ C2×C5×C7×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC5×C7ΓL(1,𝔽8)×D23
commutator, cosocle, hypocenterC7×C23C2×C3×C5×C7
FrattiniC1G
Fitting, socleC5×C72×C23C2×C3
LCSG ▷ C7×C23
UCSC1 ◁ C5×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2415

Conjugacy classes & character table

2275 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33810, 28);