Finite Group Databasebeta

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C2×H(3,𝔽4)×D59 #29495560

order15104
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C211×C42

Aliases

direct productC2×H(3,𝔽4)×D59

Splittings

FittingC2×C59×H(3,𝔽4) ⋊ C2
SylowC59 ⋊ C22×H(3,𝔽4)

Subgroups

subgroupG/H
centerC23C24×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×C59×H(3,𝔽4)C2
socleC23×C59C25
hypercenterC2×H(3,𝔽4)D59
hypocenterC59C22×H(3,𝔽4)
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×H(3,𝔽4)

10246 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

1178 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1076439);