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H(5,𝔽2)×#10596842 #34035047

order18688
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C29

Aliases

direct productH(5,𝔽2)×#10596842

Splittings

FittingH(5,𝔽2)×C73 ⋊ C8
SylowC73 ⋊ C8×H(5,𝔽2)

Subgroups

subgroupG/H
center, FrattiniC2C24×#10596842
commutator, socleC2×C73C24×C8
FittingH(5,𝔽2)×C73C8
prime radicalH(5,𝔽2)×D73C4
cosocleC2×#64408C25
hypercenterH(5,𝔽2)#10596842
hypocenterC73C8×H(5,𝔽2)
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ H(5,𝔽2)

2422 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 584

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1118631);