Finite Group Databasebeta

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H(3,ℤ/4)×#6923 #30602283

order15616
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C2×C43

Aliases

direct productH(3,ℤ/4)×#6923

Splittings

FittingC61×H(3,ℤ/4) ⋊ C4
SylowC61 ⋊ C4×H(3,ℤ/4)

Subgroups

subgroupG/H
centerC4C42×#6923
commutatorC4×C61C43
FrattiniC22×C4C22×#6923
FittingC61×H(3,ℤ/4)C4
socleC2×C61C4×#95
prime radicalC23×D61C2×D4
cosocleC22×C4×D61C23
hypercenterH(3,ℤ/4)#6923
hypocenterC61C4×H(3,ℤ/4)
LCSG ▷ C4×C61 ▷ C61
UCSC1 ◁ C4 ◁ H(3,ℤ/4)

954 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 976

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1091838);