Finite Group Databasebeta

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C2×H(5,𝔽2)×#6923 #30626729

order15616
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC2×H(5,𝔽2)×#6923
unambiguous semidirect productD61⋊(C4×H(5,𝔽2))

Splittings

FittingC2×H(5,𝔽2)×C61 ⋊ C4
SylowC61 ⋊ C2×C4×H(5,𝔽2)

Subgroups

subgroupG/H
centerC22C24×#6923
commutatorC2×C61C25×C4
FrattiniC2C25×#6923
FittingC2×H(5,𝔽2)×C61C4
socleC22×C61C24×C4
prime radicalC2×H(5,𝔽2)×D61C2
cosocleC2×D61C26
hypercenterC2×H(5,𝔽2)#6923
hypocenterC61C2×C4×H(5,𝔽2)
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×H(5,𝔽2)

12378 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 976

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1116284);