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C5×C23×ΓL(1,𝔽8)⋊D7 #46798927

order33810
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C23 · Schur multiplier (H2) = C1

Aliases

direct productC5×C23×ΓL(1,𝔽8)⋊D7
unambiguous semidirect productΓL(1,𝔽8)⋊(C5×D7×C23)

Splittings

Fitting, socle, HallC5×C72×C23 ⋊ C2×C3
derived, SylowC72 ⋊ C2×C3×C5×C23
HallC5×C7×ΓL(1,𝔽8)×C23 ⋊ C2
HallC5×C23×C7⋊D7 ⋊ C3
HallC7×ΓL(1,𝔽8)×C23 ⋊ C2×C5
HallC23×C7⋊D7 ⋊ C3×C5
HallC72×C23 ⋊ C2×C3×C5
HallC5×C7×ΓL(1,𝔽8) ⋊ C2×C23
HallC5×C7⋊D7 ⋊ C3×C23
HallC5×C72 ⋊ C2×C3×C23
HallC7×ΓL(1,𝔽8) ⋊ C2×C5×C23
HallC7⋊D7 ⋊ C3×C5×C23

Subgroups

subgroupG/H
center, hypercenterC5×C23ΓL(1,𝔽8)⋊D7
commutator, cosocle, hypocenterC72C2×C3×C5×C23
FrattiniC1G
Fitting, socleC5×C72×C23C2×C3
LCSG ▷ C72
UCSC1 ◁ C5×C23

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2415

Conjugacy classes & character table

2530 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33810, 31);