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5−1+2×ΓL(1,𝔽32) #34084273

order19375
automorphism?
homologyAbelianization (H1) = C53 · Schur multiplier (H2) = C52

Aliases

direct product5−1+2×ΓL(1,𝔽32)

Splittings

FittingC31×5−1+2 ⋊ C5
SylowC31 ⋊ C5×5−1+2

Subgroups

subgroupG/H
center, FrattiniC5C52×ΓL(1,𝔽32)
commutator, socle, cosocleC5×C31C53
FittingC31×5−1+2C5
prime radicalC52×ΓL(1,𝔽32)C5
hypercenter5−1+2ΓL(1,𝔽32)
hypocenterC31C5×5−1+2
LCSG ▷ C5×C31 ▷ C31
UCSC1 ◁ C5 ◁ 5−1+2

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 775

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19375, 50);